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First published online 15 January 2008
doi: 10.1242/jcs.021485
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Research Article |
1 Department of Medicine, University of North Carolina, Chapel Hill, NC 27599, USA
2 Cell and Molecular Physiology, University of North Carolina, Chapel Hill, NC 27599, USA
3 School of Pharmacy, University of North Carolina, Chapel Hill, NC 27599, USA
4 Department of Molecular Biomedical Sciences, North Carolina State University, Raleigh, NC 27695, USA
5 Department of Dermatology, Yale University School of Medicine, New Haven, CT 06510, USA
* Author for correspondence (e-mail: vitallie{at}med.unc.edu)
Accepted 4 November 2007
| Summary |
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Key words: Claudin, Tight junctions, Paracellular permeability
| Introduction |
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Paracellular permeability is most often measured by flux of variously sized noncharged hydrophilic tracers, including radioactively labeled urea, mannitol, inulin and/or fluorescent dextrans of various sizes (Ghandehari et al., 1997
; Sanders et al., 1995
). It has been recognized for a number of years that there is a disproportionately larger permeability for compounds smaller than mannitol (Artursson et al., 1993
; Knipp et al., 1997
; Tavelin et al., 2003
). This was most elegantly demonstrated by Watson and colleagues (Watson et al., 2001
) by profiling paracellular flux across monolayers of Caco-2 and T84 cells with a continuous series of PEG oligomers. Their results clearly showed that, in these two cell lines, permeability is biphasic, consisting of a high-capacity, size-restrictive pathway and a low capacity, size-independent pathway. The high-capacity pathway behaves as a system of small pores with radii of
4 Å. The physical basis of the low-capacity pathway is less clear. It could represent fixed (e.g. tricellular junctions) or transient breaks (e.g. during apoptosis) or a system of larger pores.
Other investigators have used a variety of techniques to determine the small pore size and have reported substantially different sizes in different cell lines, tissues and in different species. For example, Tavelin and colleagues (Tavelin et al., 2003
) used a variety of paracellular flux markers to demonstrate that the small pore radius in an intestine-like cell line called 2/4/A1 was 9 Å, whereas the Caco-2 pore size was found to be 3.7 Å. Fihn and colleagues (Fihn et al., 2000
) reported that pore size is larger in intestinal crypt (50-60 Å) than in villus cells (<6 Å). He and colleagues (He et al., 1998
) demonstrated larger paracellular pores in the small intestine of dog compared with human. However, none of these studies had the resolution of the PEG profile studies, which are able to determine the relative number of pores as a continuous function of size (Watson et al., 2001
; Watson et al., 2005
).
Along with solute flux, paracellular barrier function is commonly characterized by transepithelial electrical resistance (TER). As information has emerged about the protein components of the tight junction, many studies have demonstrated that the electrical tightness of cultured epithelial monolayers can be increased or decreased by changing the expression profiles of specific proteins (reviewed by Gonzalez-Mariscal et al., 2003
; Schneeberger and Lynch, 2004
). Interest has centered on the integral membrane proteins of tight junctions, particularly claudins, occludin and junctional adhesion molecules (JAMs) as these three proteins have been demonstrated to be components of the strands that can be visualized by freeze-fracture electron microscopy and that are the sites of the adhesive cell-to-cell barriers. Our studies (Van Itallie et al., 2001
; Colegio et al., 2002
) and those of several other groups (Amasheh et al., 2002
; Yu et al., 2003
; Hou et al., 2005
) have demonstrated that claudins can change the TER through regulation of ionic charge selectivity. For example, expression of claudin-14 in MDCK II cells (Ben Yosef et al., 2003
) increases TER fivefold by selectively decreasing paracellular permeability to cations (Na+) without changing permeability for anions (Cl–). Investigations of this type, coupled with mutational analysis of the claudin extracellular domains (Colegio et al., 2002
; Hou et al., 2005
; Alexandre et al., 2007
), provide convincing evidence that claudins line the paracellular pores. The roles of occludin (Saitou et al., 1998
; Yu et al., 2005
) and JAMs (Mandell and Parkos, 2005
) are understood less well.
Although paracellular flux of noncharged solutes and electrical resistance are both measures of permeation through the paracellular pathway, their relationship sometimes appears paradoxical. For example, it seems consistent that TER decreases at the same time that solute flux increases following exposure of T84 cell monolayers to interferon-
(Watson et al., 2005
). By contrast, there are multiple examples where changing claudin levels alters TER without any coincident changes in flux for noncharged solutes (Van Itallie et al., 2001
; Amasheh et al., 2002
) or where changes in occludin levels increase TER and flux simultaneously (Balda et al., 1996
). To better understand the relationship between TER and permeability and to begin to identify the proteins involved in the regulation of solute flux, we have adapted a method (Watson et al., 2001
) for profiling the permeability of tight junctions as a function of solute size and applied it to several different cultured epithelial cell lines and tissues. Our initial aims were to determine first whether pore size and number varied among different cell types, second whether claudins influence these properties and third how pore number is related to TER. We demonstrated previously that the electrical charge on the extracellular domains of claudins influences the permeability of ions passing through the tight junction, consistent with the idea that claudins border, or are within a few Ångstroms of, the pores (Colegio et al., 2002
). This led us to ask whether different claudins might differentially affect pore size and/or number. We chose to focus our study on claudin-2 (also known as claudin 2) as this claudin has been identified as an electrically `leaky' claudin (Furuse et al., 2001
; Amasheh et al., 2002
) and is concentrated in intestinal crypts (Holmes et al., 2006
), where larger paracellular pores have been reported (Marcial et al., 1984
). We also tested the effects of expressing claudin-4, which increases TER in MDCK II cells, and asked whether this increased TER was accompanied by a decrease in pore number or size. We found that, in all tested monolayers, the majority of solute flux occurs through pores with a common aperture radius of 4 Å. We made the novel observation that the density of small pores along the junction varies significantly among cell types. Furthermore, we found that expression of claudin-2 in MDCK cells could increase the number of small pores but that neither knockdown of claudin-2 nor expression of several other claudins could influence pore number. These findings suggest that, although claudins might be components of the small pores, other factors regulate pore number.
| Results |
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7 minutes), corresponding to a radius of
4 Å. Purified PEG28 is added before derivatization as an internal recovery standard (far-right peak in Fig. 1). We have verified that derivatization is complete, flux is linear up to 3 hours and identical in both directions, and the filter without cells shows high permeability without size selectivity (data not shown). The smallest PEG reliably detected is of radius 2.8 Å (PEG3, HPLC position verified with triethylene glycol), and the largest we studied is
7 Å (PEG25). The hydrodynamic radii (r) of PEG oligomers are related to molecular mass (M) by the relationship r (Å)=0.29M0.454 (Ruddy and Hadzija, 1992
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The number of pores but not their size differs among cell types
PEG permeability profiling offers striking insights about the size selectivity of the paracellular pathway. When Papp is plotted as a function of PEG radius (Fig. 2), two components or pathways are clearly revealed. The first has a steep negative slope, from which it is possible to calculate an approximate pore radius of 4 Å; this can be interpreted as a high-capacity system of small pores with a clearly defined aperture size. Solutes that are larger than the small pores are relatively more restricted and pass in a size-independent manner; the slope of Papp as a function of size is close to zero. This implies that their diffusion occurs through intercellular spaces that are much larger than 8 Å and that account for relatively less area than the area containing small pores. The magnitude of both pathways varies among cell types. Molecules that are smaller than the pores (PEG3-PEG5) can also pass through the nonrestrictive pathway; this contribution must be subtracted from the first phase to determine their permeability specifically through the pores as well as to derive the pore size. To correct for this contribution, the second phase (
4 Å) is analyzed by linear regression, and extrapolated values are subtracted from the first phase.
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We have extended the published studies of the human intestinal cell lines Caco-2 and T84 (Watson et al., 2001
) to include ex vivo porcine ileal mucosa and three renal tubular epithelial lines, namely porcine LLC-PK1 cells (data not shown) and two clones of canine MDCK cells, low-TER MDCK II and high-TER MDCK C7 (Gekle et al., 1994
; Wunsch et al., 1995
) (Fig. 2). The key observations are, first, that all five cell lines have a similar pore radius of
4 Å. Ileum (and possibly Caco-2) has an additional cut-off of
6.5 Å (Fig. 2). Second, the number of pores per area of the monolayer, which is proportional to Papp for solutes that are of radius <4 Å, is strikingly different among cell types. It should be noted that pore number is a functional definition, not a structural one, as small pores could theoretically have open or closed probabilities that differ among the different cell lines. Third, the nondiscriminating pathway is also variable in magnitude, but less so than the small pores. We also attempted to characterize the size selectivity of HUVECs, a commonly used human umbilical vein endothelial cell line. However, despite establishing a low but detectable TER, HUVEC monolayers showed little discrimination in the range 2.3-7.0 Å, implying that their predominant paracellular spaces are larger than 7 Å.
Pore density along the junction differs among cell types
The difference in pore number per unit area among cell lines is not the result of differences in the linear length of junction per unit area; instead our data lead to the novel conclusion that cell types can differ in the apparent density of pores along the junction (Fig. 3). Junction length per area was derived from monolayers immunolabeled for a marker of tight junctions and analyzed by imaging software (Fig. 3B). Caco-2 cells are slightly smaller than both clones of MDCK cells (Fig. 3A) and thus have slightly more junctional length through which PEGs can diffuse (Fig. 3B). In order to compare the relative number of pores per unit area, we compare the Papp for the 3.5 Å species, which should be directly proportional to the number of pores. When the Papp for PEG5 is compared among cell types (Fig. 3D), Caco-2 monolayers are seen to have
12-fold more pores per area than MDCK C7; MDCK II monolayers are intermediate. When Papp is corrected for differences in the length of junction per area, Caco-2 cells still contain
7-fold more pores per length of junction than MDCK C7 cells; the density of pores along MDCK II cell junctions is intermediate. Microanatomical differences, including differences in tight junction strand number or tortuosity that we have not assessed might contribute to the apparent differences in pore density; however, previous electron-microscopic comparison of high-resistance (similar to C7 cells) and low-resistance MDCK cell lines did not demonstrate any anatomic difference in the morphology of the tight junctions (Stevenson et al., 1988
) in spite of the observed difference in apparent TER.
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TER is inversely proportional to the current that flows in response to an applied voltage; in physiologic solutions, this current is primarily carried by Na+ (0.95 Å) and Cl– (1.81 Å) ions (Hille, 2001
) and thus mainly conducted through the small pores. Therefore, the TER of a monolayer might be expected to be inversely related to the number of pores as defined by flux studies; however, we observed that this is not necessarily true. While MDCK C7 monolayers do have a higher TER (Fig. 3C) and fewer pores than either Caco-2 or MDCK II monolayers (Fig. 3D), Caco-2 monolayers actually have both a much higher TER and higher number of pores than MDCK II monolayers. Assuming that claudins are a major component of pores, we speculate that this apparent inconsistency results from the charge discrimination characteristics of different claudins expressed in Caco-2 versus MDCK II cells. This has an impact on TER but not the Papp of non-charged PEGs. TER could therefore be both a function of claudin charge selectivity and of the number of pores, each of which can vary independently.
Induction of claudin-2, but not claudin-4, increases the number of small pores
MDCK II and MDCK C7 monolayers differ significantly in TER and in relative pore number (Fig. 3C,D), despite having approximately the same length of junction per monolayer area. One possible reason for the difference in porosity might be a difference in the expression profiles of their tight junction proteins. Amasheh and colleagues (Amasheh et al., 2002
) demonstrated that the levels of claudin-2, but not claudin-3, differ between MDCK II and C7 cells. We extended this comparison to include claudins-4 and -7, plus ZO-1, occludin and E-cadherin (Fig. 4). The largest differences were that MDCK C7 cells have much lower levels of claudin-2 (
7%) and claudin-7 (
30%) and much higher levels of claudin-4 protein (increased by more than sixfold). The immunofluorescent localizations of the various claudins in the two cell lines were similar (supplementary material Fig. S1). If one assumes that pore density is a function of the number of pore-forming claudins in a background of non-permeant strand proteins (occludin or JAM, for example), then it might be possible to alter pore number by changing the composition of the strands through expression of particular claudins. Interestingly, expression of claudin-2 in high-TER MDCK cells results in decreased TER (Furuse et al., 2001
; Amasheh et al., 2002
), whereas siRNA-mediated knockdown of claudin-2 in low-TER MDCK II cells increases TER (Hou et al., 2006
). This led us to test the possibility that increasing levels of claudin-2 might increase the number of small pores.
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PEG profiling and Papp were determined (Fig. 5) in MDCK II monolayers stably expressing claudins-2, -4, -14 and -18, in MDCK C7 cells expressing claudin-2 and in MDCK II cells in which expression of claudin-2 was inhibited by using RNAi. Immunoblots (Fig. 5A) reveal at least a fourfold increase in claudin-2 and claudin-4 in representative MDCK cell clones and a 90% decrease in claudin-2 in the RNAi knockdown cells; in no condition was there much change in occludin, an unrelated transmembrane protein in the strands (Fig. 5A), or in the levels of claudins-1 or -3. Induction of claudin-4 resulted in a twofold decrease in the levels of claudin-7; however, the physiological consequences of the decrease are unclear as claudin-7 is located all along the basolateral membrane of MDCK cells (supplementary material Fig. S2). The effects of expression of claudins-2 and -4 on TER have been reported previously (Colegio et al., 2003
; Van Itallie et al., 2001
; Amasheh et al., 2002
; Hou et al., 2006
); the present study confirmed that expression of claudin-2 in low-resistance MDCK II cells caused a slight increase in TER, whereas expression of the same claudin in high-resistance MDCK C7 cells resulted in a significant drop in resistance. Expression of claudin-4 and knockdown of expression of claudin-2 in MDCK II cells resulted in twofold and threefold increases in TER, respectively (Fig. 5B).
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In contrast to the effects of overexpression of claudin-2, knockdown of claudin-2 levels in MDCK II cells does not change the apparent pore number (Fig. 5D). In addition, there was no change in Papp profiles in MDCK II cells induced to express claudins-4 (Fig. 5D), -14 or -18 (data not shown). Morphometric analysis of the length of tight junctions before and after induction of any of the claudins did not show a significant change (data not shown). Together, these data suggest that the ability of claudin-2 to increase pore number might be a special characteristic of this claudin and that, even though knockdown of claudin-2 or overexpression of claudins-4, -14 and -18 can alter the electrical characteristics of the pores, they do not affect pore size or number. Of note, increasing the level of claudin-2 did not alter the flux of mannitol (Fig. 5E, 4.2 Å), a widely used permeability marker – revealing that mannitol flux measurements detect the magnitude of the size-independent pathway but not the small pore system.
| Discussion |
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4 Å. Furthermore, we demonstrate that the number of pores is quite variable among cell lines and does not correlate with either the length of junction or with TER. This implies that tight junctions can vary in the density of pores along the cell-cell contact. We also observed that increasing the level of claudin-2, but not -4, -14 and -18, in MDCK cells increased the number of pores without altering the pore size or significantly altering Papp for PEGs that are larger than the pore. Although it is possible that pore number is regulated by claudins that we have not tested, the simplest explanation for our findings is that claudins are constituents of the pores of radius 4 Å but that, overall, pore number within a single cell type is tightly regulated, perhaps by structural constraints, by other strand proteins or by cytosolic or regulatory components.
The accuracy of our assessment of pore size is limited by our use of a single type of probe; however, the validity of the use of PEGs as flux markers has been verified by others (Watson et al., 2001
). In any case, the goal of the present study was to apply a single assay to allow comparison of relative pore sizes after different experimental manipulations rather than providing a measurement of exact pore size. However, an unexpected outcome was that all cell lines that we examined, as well as pig ileum, had identical restrictive pore sizes. With the exception of the analysis of T84 and Caco-2 cells (Watson et al., 2001
), there has been little systematic comparison of pore size across different experimental systems. One exception is a comparison of PEG absorption in dog, rat and human gut, which found species-specific differences in pore size (He et al., 1998
). Other studies demonstrated the presence of larger pores in intestinal crypts when compared with villus cells (Fihn et al., 2000
). It is possible that tissues have a more complex pore composition than the homogeneous cell lines we examined as our results in pig ileum suggest the existence of a second restrictive pore with a size cut-off of radius
6-7 Å.
Pore size might be a function of claudin structure. As claudin expression in non-epithelial fibroblasts can recapitulate the strand morphology of tight junctions (Furuse et al., 1998
), we have assumed that the tight junction barrier comprises continuous claudin polymers that organize to form paracellular pores. Many studies have now demonstrated that claudins influence paracellular ionic selectivity and TER – it would seem reasonable to assume that these would be the same pores that regulate the flux of the small PEGs. As all claudins have extracellular loops of nearly identical size, it is possible that pore size is a function of the geometry of claudin-claudin interactions and thus would be structurally similar for all claudins. We have attempted to test this hypothesis by overexpressing PMP-22, a distant member of the claudin family, which is a component not only of peripheral myelin but also of epithelial tight junctions (Notterpek et al., 2001
) and which has smaller extracellular domains than are characteristic of conventional claudins (56 compared with 77 amino acids for loop 1 plus loop 2). We found that overexpression of PMP-22 did not change the pore size in MDCK II cells; however, the overexpression was in the background of endogenous claudins and thus their presence might have defined the majority pore size. To test this more explicitly, we would need to perform these studies in a cell background where PMP-22 is the predominant claudin; this will be attempted in future experiments. It is also possible, however, in spite of the fact that claudins form the structural basis of the tight junction, and regulate paracellular ion selectivity, that the small pores measured by PEG flux represent a separate passage through the tight junction.
Even if small pore size is determined by claudin interactions, there could still be a second set (or more) of larger size-restrictive pores defined by interactions of other tight junction proteins or by modifiers of claudin-claudin interactions. The characterization of larger pores will depend on the ability to profile the paracellular permeation of species of higher molecular mass than the PEGs used in this study. Although profiling of this type will be less sensitive because of the lower capacity of this pathway, it is important as changes in the flux of larger molecules (e.g. antigens) is likely to be of great pathologic significance and is important for drug delivery.
The lack of relationship between TER and pore number was more dramatic than we had anticipated. For example, MDCK II cells, which have a fivefold lower TER than Caco-2 cells, also have fewer pores. The simplest interpretation is that TER is regulated by the ion selectivity of the pores, not just their number. In this model, tight junctions in Caco-2 cells would be expected to comprise claudins that create a high pore density and permeability for noncharged solutes but whose pores create a high TER by restricting paracellular ion permeability. Alternatively, there has long been conjecture that the paracellular pores fluctuate between an open and closed state (Claude, 1978
); pores in Caco-2 cells might be regulated such that they have a higher open probability than in MDCK cells. Additionally, although claudin expression can recapitulate tight junction fibrils in fibroblasts (Furuse et al., 1998
), in epithelial cells, the fibrils are known to contain at least occludin (Furuse et al., 1993
) and JAM (Itoh et al., 2001
). It is possible that differences in non-claudin composition or organization contribute to differences in porosity. Finally, it is also possible that PEG flux measures a separate, claudin-independent pathway through the tight junction. It is difficult to test these various ideas as we still lack basic information about how proteins in the barrier strands are organized.
Expression of claudin-2 resulted in a significant increase in small pore number with no change in pore size. This increase could be due to a change in the absolute number of small pores or might represent the ability of claudin-2 expression to modify pore characteristics such that more pores are available for noncharged solutes. It was previously speculated that the ability of claudin-2 to decrease TER in MDCK C7 cells resulted from its lack of adhesion to other claudins and the consequent formation of breaks in the barrier (Furuse et al., 2001
). Although this is a possible mechanism for how induction of claudin-2 might lead to increased pore number, the observed pore size does not change, suggesting that the space created by mismatched claudins is indistinguishable from pores formed in the absence of claudin-2, as seen in the MDCK C7 or Caco-2 cells. Additionally, the increase in pore number was specific for the small pores as we found that overexpression of claudin-2 did not change the flux of mannitol, and Amasheh and colleagues (Amasheh et al., 2002
) found no change in the flux of 4-kDa dextran; both these markers report flux across the size-independent pathway.
In contrast to the effect of expressing claudin-2, the overexpression of claudin-4, -14 and -18 had no effect on pore number or pore size, despite significant effects on TER. This lack of effect could mean that these claudins replace rather than add to existing claudins in the tight junction strands. By substituting for an endogenous claudin that is less ion permeable, expression of these claudins might promote greater electrical tightness, while maintaining the same permeability for nonionic solutes as the endogenous charge-leaky claudin. Similar to the lack of effect of overexpression of claudin-4, knockdown of claudin-2 failed to decrease pore number in MDCK cells. Again, removal of claudin-2 might result in replacement by other claudins that are less cation permeable, resulting in no net change in pore number but resulting in increased TER.
These speculations are not yet supported by experimental evidence as we lack a complete description of claudin expression in MDCK cells and we could observe little compensatory changes in the levels of the other claudins for which we have antibodies. Without an exhaustive comparison of claudin levels, it would be difficult to demonstrate conclusively the difference between substitution and addition, especially as the localization of claudin is not limited to tight junctions, presumably the sites at which they regulate permeability. However, Angelow and colleagues have recently demonstrated that expressed claudin-8 in MDCK II cells replaces endogenous claudin-2 (Angelow et al., 2007
), consistent with this possibility.
Some special characteristic of claudin-2 might allow it (and perhaps other as-yet-untested claudins) to be able to add pores. This ability could be related to claudin-2 interactions with cytosolic proteins as preliminary data demonstrate that removal of the C-terminal PDZ-binding motif abrogates the increase in pore number seen with expression of full-length claudin-2 (data not shown). There is also the possibility that expression of claudin-2 acts indirectly to affect pore properties, by affecting a non-claudin pore system or perhaps regulating pore behavior. Several reports have implicated Rho in the regulation of paracellular flux without accompanying changes in TER (Hasegawa et al., 1999
), perhaps through the activation of a recently identified tight junction GDP-GTP exchange factor (Benais-Pont et al., 2003
). However, a limitation of these studies was their use of markers of higher molecular mass that did not allow measurement of flux through the system of small pores.
In conclusion, PEG profiling reveals several novel insights about the tight junction barrier. A high-capacity pathway for solutes of radius less than 4 Å is responsible for conducting small non-charged solutes and, presumably, small electrolytes. The density of pores along the tight junction varies among cell types and can be increased by expression of claudin-2 but not several other claudins. This, together with their capacity for charge discrimination, implicates claudins in forming the pores but does not rule out a role for other proteins in regulating paracellular flux. It is clear that, although the description of the epithelial barrier properties as `leaky' or `tight' is useful, a more accurate characterization of paracellular properties should also take into account the magnitude of both the pore pathway and size-independent pathway and the charge selectivity of the pores. Further studies should be directed at understanding physiologic and pathologic processes that control the characteristics of both pathways.
| Materials and Methods |
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Porcine ileal mucosa was prepared for barrier function studies as described elsewhere (Gookin et al., 2006
); the TER, short circuit current (Isc), [3H]-mannitol and PEG fluxes were determined. The TER and Isc were stable throughout two-hour flux studies.
PEG permeability assay
The polyethylene glycol flux assay was substantially modified from that described by Watson and colleagues (Watson et al., 2001
). In place of LC-MS analysis, we adapted a method to modify PEGs fluorescently after the flux protocol with 1-NIC and then resolve the sizes by HPLC and quantify each by fluorescence emission (Rissler et al., 1998
). Cell monolayers were rinsed twice at 37°C in Hanks' balanced salt solution (InVitrogen) and preincubated in Hanks' for 30 minutes. The salt solution was removed and replaced with fresh Hanks' or with Hanks' containing a 5 mg/ml mixture of PEG200, PEG400 and PEG900 (Fluka) at a ratio of 2:0.5:1 (by weight). PEGs were added either to the basal or the apical chambers; the level of flux showed no polarity. Samples were removed from the donor and acceptor compartments at 0, 60, 120 and 180 minutes and an internal standard (20 µg purified PEG28, Polypure AS, Oslo, Norway) was added to all samples. After storage at –20°C, samples were thawed and dried at 55°C in a water bath under a stream of N2. PEGs were derivatized by addition of 10 µl 1-NIC (Acros Organics) in 100 µl of acetone. Samples were vortexed for 4 hours at room temperature; then 50 µl of methanol and 500 µl H2O were added to quench excess reagent and samples were vortexed vigorously. Following two extractions with diethylether, 100 µl of the aqueous phase was analyzed on a bare silica column (Waters Spherisorb 5.0 µm Silica column, 4.6x150 mm, Waters Corporation, Milford, MA) by HPLC (Agilent Technologies) and peaks quantified by fluorescence emission (Agilent HPCHEM station, excitation=232 nm, emission=358 nm). Papp was determined as (dQ/dt)/AxC0 where A=filter area and C0 is the initial concentration in the donor compartment. C0 did not change significantly over the 120 minute flux study.
To correct the Papp of the size-dependent first phase, the second phase is extended after linear regression and subtracted from the first phase. The aqueous pore radius was calculated from the ratio of the corrected paracellular permeabilities of pairs of two small PEG species (2.8, 3.2, 3.5 or 3.7), applying a sieving function as described in equations 7 (see Renken, 1954
) and 8 (see Knipp et al., 1997
). Corrected values for the 3.2 or 3.5 Å species were used to compare flux in Figs 3 and 5 and represent the permeability for a size that freely permeates the pore.
| Acknowledgments |
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| Footnotes |
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| References |
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