The effect of auxiliary conditions on intestinal unstirred layer diffusion modelled by numerical simulation.

Estimation of intestinal unstirred layer thickness usually involves inducing transmural potential difference changes by altering the content of the solution used to perfuse the small intestine. Osmotically active solutes, such as mannitol, when added to the luminal solution diffuse across the unstirred water layer (UWL) and induce osmotically dependent changes in potential difference. As an alternative procedure, the sodium ion in the luminal fluid can be replaced by another ion. As the sodium ion diffuses out of the UWL, the change in concentration next to the intestinal membrane alters the transmural potential difference. In both cases, UWL thickness is calculated from the time course of the potential difference changes, using a solution to the diffusion equation. The diffusion equation solution which allows the calculation of intestinal unstirred layer thickness was examined by simulation, using the method of numerical solutions. This process readily allows examination of the time course of diffusion under various imposed circumstances. The existing model for diffusion across the unstirred layer is based on auxiliary conditions which are unlikely to be fulfilled in the same intestine. The present simulation additionally incorporated the effects of membrane permeability, fluid absorption and less than instantaneous bulk phase concentration change. Simulation indicated that changes within the physiologically relevant range in the chosen auxiliary conditions (with the real unstirred layer length kept constant) can alter estimates of the apparent half-time. Consequently, changes in parameters unassociated with the unstirred layer would be misconstrued as alterations in unstirred layer thickness.     

Potassium ion accumulation at the external surface of the nodal membrane in frog myelinated fibers.

Potassium accumulation associated with outward membrane potassium current was investigated experimentally in myelinated fibers and analyzed in terms of two models-three-compartment and diffusion in an unstirred layer. In the myelinated fibers, as in squid giant axons, the three-compartment model satisfactorily describes potassium accumulation. Within this framework the average space thickness, theta, in frog was 5,900 +/- 700 A, while the permeability coefficient of the external barrier, PK, was (1.5 +/- 0.1) X 10(-2) cm/s. The model of ionic diffusion in an unstirred aqueous layer adjacent to the axolemma, as an alternative explanation for ion accumulation, was also consistent with the experimental data, provided that D, the diffusion constant, was (1.8 +/- 0.2) X 10(-6) cm/s and l, the unstirred layer thickness, was 1.4 +/- 0.1 micron, i.e., similar to the depth of the nodal gap. An empirical equation relating the extent of potassium accumulation to the amplitude and duration of depolarization is given.     

Aging: its influence on the intestinal unstirred water layer thickness, surface area, and resistance in the unanesthetized rat

The intestinal absorption of some nutrients changes with aging. As the unstirred water layer (UWL) is an important rate limiting step in the absorption of nutrients in general and of lipid soluble nutrients in particular, we investigated possible changes in the UWL dimensions in the aging rat in vivo. We measured the thickness (d) of the UWL using rapid changes in the luminal sodium concentration to induce changes in the transmucosal potential differences. We assessed the surface area (Sw) and resistance (d/SwD) of the UWL at varying flow rates by using increasingly lipophilic medium chain saturated alcohols as probes. At high UWL resistance, d decreased from 318 to 268 microns between 1 and 29 months of age. As the animals aged, Sw changed from 114 to 106 cm2/100 cm and from 262 to 214 cm2/100 cm at low and high flow rates, respectively, using dodecanol as a probe. The resistance of the UWL (d/SwD) remained relatively stable at all ages studied. These experiments demonstrate that age-related changes in absorption are dependent on the aqueous diffusion coefficient and degree of lipid solubility of the specific nutrients. At low UWL resistance, absorption of compounds with higher diffusion coefficients and greater aqueous solubility is decreased with aging. In contrast, previous studies have demonstrated that the absorption of nutrients with low diffusion coefficients and high lipid solubility increases with aging especially when the resistance of the UWL is high.     

The water permeability of toad urinary bladder. I. Permeability of barriers in series with the luminal membrane

Antidiuretic hormone (ADH) induces a large increase in the water permeability of the luminal membrane of toad urinary bladder. Measured values of the diffusional water permeability coefficient, Pd(w), are spuriously low, however, because of barriers within the tissue, in series with the luminal membrane, that impede diffusion. We have now determined the water permeability coefficient of these series barriers in fully stretched bladders and find it to be approximately 6.3 X 10(- 4) cm/s. This is equivalent to an unstirred aqueous layer of approximately 400 microns. On the other hand, the permeability coefficient of the bladder to a lipophilic molecule, hexanol, is approximately 9.0 X 10(-4) cm/s. This is equivalent to an unstirred aqueous layer of only 100 microns. The much smaller hindrance to hexanol diffusion than to water diffusion by the series barriers implies a lipophilic component to the barriers. We suggest that membrane-enclosed organelles may be so tightly packed within the cytoplasm of granular epithelial cells that they offer a substantial impediment to diffusion of water through the cell. Alternatively, the lipophilic component of the barrier could be the plasma membranes of the basal cells, which cover most of the basement membrane and thereby may restrict water transport to the narrow spaces between basal and granular cells.     

On the large error introduced in the estimate of the density of membrane pores from permeability measurements when diffusion in "unstirred layer" within the cells is disregarded

After the development of the "black lipid membrane" techniques, studies of the permeability of labeled water and nonelectrolytes across these artificial membranes have yielded permeability constants comparable in magnitude to those obtained from tracer studies of living cell membranes. This general agreement has affirmed the belief that the living cell membranes are indeed closely similar to these bilayer phospholipid membranes. In this report, we draw attention to a hidden assumption behind such comparisons made: the assumption that labeled material passing through the cell membrane barriers instantly reaches diffusion equilibrium inside the cell. The permeability constants to labeled water (and nonelectrolytes) across lipid layers were obtained using setups in which the lipid membrane was sandwiched between aqueous compartments both of which were vigorously stirred. In studies of permeability of living cell membranes only the outside solution was stirred, the intracellular water remained stationary. Yet the calculations of permeability constants of the cell membrane were made with the tacit assumption, that once the labeled materials pass through the cell membrane, they were instantly mixed with the entire cell contents as if a stirrer operating at infinite speed had been present inside the cells. Ignoring this unstirred condition of the intracellular water, in fact, lumped all the real-life delay due to diffusion in the cytoplasm and added it to the resistance to diffusion of the membrane barrier. The result is an estimated membrane permeability to labeled water (and nonelectrolytes) many times slower than it actually is. The present report begins with a detailed analysis of a specific case: tritiated water diffusion from giant barnacle muscle fibers and two non-living models, one real, one imagined.(ABSTRACT TRUNCATED AT 250 WORDS)     

The Effect of the Unstirred Layer on Human Red Cell Water Permeability

A study has been made of water entry into human red blood cells under an osmotic pressure gradient. The measurements were made using a rapid reaction stop flow apparatus, whose construction, calibration, and performance are described in detail. Red cell volume changes were determined from 90° scattered light. The permeability coefficient for water entry under a relative isosmolar concentration of 1 to 1.5 was found to be 0.22 ± 0.01 cm⁴/sec osmol, which agrees well with our previously published value. The experiments were also designed to measure the thickness of the unstirred layer around the6 red cells. This was found to be 5.5 ± 0.8 µ under the present experimental conditions. It is concluded that our previously measured permeability coefficient for water entrance under a diffusion gradient does not require correction on account of the unstirred layer.     

Transport methods for probing the barrier domain of lipid bilayer membranes.

Two experimental techniques have been utilized to explore the barrier properties of lecithin/decane bilayer membranes with the aim of determining the contributions of various domains within the bilayer to the overall barrier. The thickness of lecithin/decane bilayers was systematically varied by modulating the chemical potential of decane in the annulus surrounding the bilayer using different mole fractions of squalene in decane. The dependence of permeability of a model permeant (acetamide) on the thickness of the solvent-filled region of the bilayer was assessed in these bilayers to determine the contribution of this region to the overall barrier. The flux of acetamide was found to vary linearly with bilayer area with Pm = (2.9 +/- 0.3) x 10(-4) cm s-1, after correcting for diffusion through unstirred water layers. The ratio between the overall membrane permeability coefficient and that calculated for diffusion through the hydrocarbon core in membranes having maximum thickness was 0.24, suggesting that the solvent domain contributes only slightly to the overall barrier properties. Consistent with these results, the permeability of acetamide was found to be independent of bilayer thickness. The relative contributions of the bilayer interface and ordered hydrocarbon regions to the transport barrier may be evaluated qualitatively by exploring the effective chemical nature of the barrier microenvironment. This may be probed by comparing functional group contributions to transport with those obtained for partitioning between water and various model bulk solvents ranging in polarity or hydrogen-bonding potential. A novel approach is described for obtaining group contributions to transport using ionizable permeants and pH adjustment. Using this approach, bilayer permeability coefficients of p-toluic acid and p-hydroxymethyl benzoic acid were determined to be 1.1 +/- 0.2 cm s-1 and (1.6 +/- 0.4) x 10(-3) cm s-1, respectively. From these values, the -OH group contribution to bilayer transport [delta(delta G0-OH)] was found to be 3.9 kcal/mol. This result suggests that the barrier region of the bilayer does not resemble the hydrogen-bonding environment found in octanol, but is somewhat less selective (more polar) than a hydrocarbon solvent.     

Comparative assessment of the resistance of the unstirred water layer to solute transport between two different intestinal perfusion systems

The resistance of the unstirred water layer to solute transport was estimated in two different intestinal single-pass perfusion systems for a comparative study, using D-glucose as a model compound. One is a well established perfusion system in anesthetized rats as a standard (system A). The other is the one in unanesthetized rats for comparison (system B). It was demonstrated that in system B as well as in system A the resistance of the unstirred water layer to D-glucose transport should be taken into account and this resistance, accordingly, the effective thickness of the unstirred water layer (delta) which is assumed to be in proportion to its resistance, could be described as a function of the perfusion rate by using a film model. The delta decreased with increasing perfusion rate and was larger in system A than in system B at each perfusion rate; 785 microns in system A versus 319 microns in system B at the perfusion rate of 0.16 ml/min and 337 microns versus 184 micron at that of 2.95 ml/min. Thus in system B the effective thickness, accordingly, the resistance, of the unstirred water layer was reduced to about 50% of that in system A, but the resistance of the unstirred water layer could still account for 85% of the total resistance at the maximum as far as D-glucose absorption was concerned, while 93% in system A. These results suggest that, compared with perfusion experiments in anesthetized rats (system A), the resistance of the unstirred water layer is reduced but cannot be left out of consideration even if perfusion experiments are performed in unanesthetized rats (system B). And the lower resistance of the unstirred water layer in system B was attributed to a turbulent flow in contrary to a laminar flow in system A.     

Evaluation of basement membrane degradation during TNF-alpha-induced increase in epithelial permeability

We evaluated whether tumor necrosis factor (TNF)-alpha induces an increase in permeability of an alveolar epithelial monolayer via gelatinase secretion and basement membrane degradation. Gelatinase secretion and epithelial permeability to radiolabeled albumin under unstimulated and TNF-alpha-stimulated conditions of an A549 human epithelial cell line were evaluated in vitro. TNF-alpha induced both upregulation of a 92-kDa gelatinolytic activity (pro form in cell supernatant and activated form in extracellular matrix) and an increase in the epithelial permeability coefficient compared with the unstimulated condition (control: 1.34 +/- 0.04 x 10(-6) cm/s; 1 microg/ml TNF-alpha: 1.47 +/- 0.05 x 10(-6) cm/s, P < 0.05). The permeability increase in the TNF-alpha-stimulated condition involved both paracellular permeability, with gap formation visualized by actin cytoskeleton staining, and basement membrane permeability, with an increase in the basement membrane permeability coefficient (determined after cell removal; control: 2.58 +/- 0.07 x 10(-6) cm/s; 1 microg/ml TNF-alpha: 2.82 +/- 0.02.10(-6) x cm/s, P < 0.05). Because addition of gelatinase inhibitors [tissue inhibitor of metalloproteinase (TIMP)-1 or BB-3103] to cell supernatants failed to inhibit the permeability increase, the gelatinase-inhibitor balance in the cellular microenvironment was further evaluated by cell culture on a radiolabeled collagen matrix. In the unstimulated condition, spontaneous collagenolytic activity inhibited by addition to the matrix of 1 microg/ml TIMP-1 or 10(-6) M BB-3103 was found. TNF-alpha failed to increase this collagenolytic activity because it was associated with dose-dependent upregulation of TIMP-1 secretion by alveolar epithelial cells. In conclusion, induction by TNF-alpha of upregulation of both the 92-kDa gelatinase and its inhibitor TIMP-1 results in maintenance of the gelatinase-inhibitor balance, indicating that basement membrane degradation does not mediate the TNF-alpha-induced increase in alveolar epithelial monolayer permeability.     

Osmosis in Cortical Collecting Tubules : A Theoretical and Experimental Analysis of the Osmotic Transient Phenomenon

This paper reports a theoretical analysis of osmotic transients and an experimental evaluation both of rapid time resolution of lumen to bath osmosis and of bidirectional steady-state osmosis in isolated rabbit cortical collecting tubules exposed to antidiuretic hormone (ADH). For the case of a membrane in series with unstirred layers, there may be considerable differences between initial and steady-state osmotic flows (i.e., the osmotic transient phenomenon), because the solute concentrations at the interfaces between membrane and unstirred layers may vary with time. A numerical solution of the equation of continuity provided a means for computing these time-dependent values, and, accordingly, the variation of osmotic flow with time for a given set of parameters including: P_f (cm s^–1), the osmotic water permeability coefficient, the bulk phase solute concentrations, the unstirred layer thickness on either side of the membrane, and the fractional areas available for volume flow in the unstirred layers. The analyses provide a quantitative frame of reference for evaluating osmotic transients observed in epithelia in series with asymmetrical unstirred layers and indicate that, for such epithelia, P_f determinations from steady-state osmotic flows may result in gross underestimates of osmotic water permeability. In earlier studies, we suggested that the discrepancy between the ADH-dependent values of P_f and P_DDw (cm s^–1, diffusional water permeability coefficient) was the consequence of cellular constraints to diffusion. In the present experiments, no transients were detectable 20–30 s after initiating ADH-dependent lumen to bath osmosis; and steady-state ADH-dependent osmotic flows from bath to lumen and lumen to bath were linear and symmetrical. An evaluation of these data in terms of the analytical model indicates: First, cellular constraints to diffusion in cortical collecting tubules could be rationalized in terms of a 25-fold reduction in the area of the cell layer available for water transport, possibly due in part to transcellular shunting of osmotic flow; and second, such cellular constraints resulted in relatively small, approximately 15%, underestimates of P_f.     

Determinants of intestinal mucosal uptake of short- and medium-chain fatty acids and alcohols

Uptake rates across the jejunal brush border have been measured for water-soluble fatty acids and alcohols and analyzed to determine the relative roles of the unstirred water layer and the lipid cell membrane as determinants of the intestinal absorptive process. Initial studies involving measurement of time courses of electrical transients developed across the intestine exposed to poorly permeant solute molecules showed no anomalous discrimination of probe molecules of different size or charge. This finding suggests that the diffusion barrier in the intestine can be considered as an unstirred water layer. Next, uptake rates of fatty acid were found to be linear with respect to concentration of the test solute, demonstrated no competitive inhibition or contralateral stimulation, had low temperature dependency, and were insensitive to metabolic inhibition, indicating that uptake proceeds by passive diffusion. Passive permeability coefficients, *P, varied from 22 +/- 1.4 to 395 +/- 9.2 nmoles.min(-1).100 mg(-1).mm(-1) for the saturated fatty acids 2:0 through 12:0 and from 119 +/- 3.3 to 581 +/- 45.2 for the saturated alcohols 6:0 through 10:0. Vigorous stirring of the bulk buffer solution enhanced *P values in direct proportion to chain length while the presence of bile acid micelles depressed apparent permeability coefficients in proportion to fatty acid chain length. These results demonstrate that uptake of short-chain fatty acid monomers is rate limited by the lipid cell membrane but diffusion through the unstirred water layer becomes increasingly rate limiting as the chain length increases. It is also possible to conclude from these data that diffusion through the unstirred water layer becomes totally rate limiting for uptake of long-chain fatty acid monomers of physiological importance.     

Diffusion from a Circular Stoma through a Boundary Layer: A FIELD-THEORETICAL ANALYSIS

The case of diffusion of a gas from a single circular stoma through an unstirred boundary layer of finite thickness into a perfectly stirred atmosphere free of convective effects is examined theoretically, with the gas assumed to be at constant concentration across the stoma. The analysis employs a mathematical solution to an analogous problem in electrostatic physics previously obtained by Kuz'min (1972 Sov Phys Tech Phys 17: 473-476). The diffusion flux is shown to be no more than 1% greater than that into a perfectly unstirred atmosphere if the boundary layer is thicker than 40 times the stomatal radius. Under the conditions assumed, for realistic boundary-layer and stomatal dimensions, taking the diffusion flux through the boundary layer to be linear with the stomatal radius would usually involve no significant error. This result may indicate that the principal effect of wind velocity on mass exchange between leaf and atmosphere may be exerted through influencing convection outside the boundary layer rather than through determining the thickness of that layer.     

Limitations of the Eadie-Hofstee plot to estimate kinetic parameters of intestinal transport in the presence of an unstirred water layer

Summary In the presence of an intestinal unstirred water layer, the relationship between substrate concentration (C ₁) and unidirectional flux (J _d) is not described by the equation for a rectangular hyperbole. Accordingly, transformations of the Michaelis-Menten equation may not necessarily be linear and may lead to serious errors in the estimation of the affinity constant (K _m) and maximal transport rate (J _d ^m ) of carrier-mediated processes. An equation has previously been derived which describedJ _d under conditions of varying effective thickness or surface area of the unstirred water layer, the free diffusion coefficient of the probe molecule, and the distribution of transport sites along the villus. These theoretical curves have been analyzed by using the Eadie-Hofstee transformation (J _d vs. J_d/C₁) of the Michaelis-Menten equation. Use of this plot leads to serious discrepancies between the true and apparent affinity constants and between true and apparent maximal transport rates. These differences are further magnified by failure to correct for the contribution of passive permeation. The Eadie-Hofstee plot is of use, however, to infer certain qualitative characteristics of active transport processes, such as the variation in affinity constants and overlying resistance of the unstirred water layer at different sites along the villus and to predict the adequacy of the correction for the contribution of passive permeation.Abbreviations Used in the Text C ₁ Concentration of the probe molecule in the bulk phase - C ₂ Concentration of the probe molecule at the aqueous-membrane interface - d Effective thickness of UWL - D Free diffusion coefficient - d ⁿ d atn th segment of the villus - f _n Proportion of total carrier transport sites present on each segment of villus - J Unidirectional flux of probe molecule, uncorrected for surface area - J _d Unidirectional flux of probe molecule determined experimentally, corrected for surface area - J _d ^m Maximal transport rate, corrected for surface area - J _d ^m* Apparent maximal transport rate - J ^m Maximal transport rate, uncorrected for surface area - K _m Michaelis constant (true affinity constant) - K _m ^* Apparent affinity constant - K _m ⁿ K _m atnth segment of the villus - n The perpendicular height of the villus was divided into ten equal segments numberedn ₁ ton ₁₀ - p Passive permeability coefficient - S _m Functional surface area of the membrane - S _w Effective surface of UWL - S _w ⁿ S _w atnth segment of the villus - UWL Intestinal unstirred water layer     

Kinetic constants for intestinal transport of four monosaccharides determined under conditions of variable effective resistance of the unstirred water layer

Summary Theoretical considerations have suggested that variations in the resistance of the unstirred water layer (UWL) have a profound effect on the kinetic constants of intestinal transport. In this study, a previously validatedin vitro technique was employed to determine the unidirectional flux rate of glucose, galactose, 3-O-methyl glucose and fructose into the rabbit jejunum under carefully-defined conditions of stirring of the bulk phase known to yield different values for the effective resistance of the UWL. For each monosaccharide, uptake is much greater when the resistance of the UWL is low than when high. The maximal transport rate,J _d ^m , of glucose was half as large as theJ _d ^m of galactose and 3-O-methyl glucose (3-O-MG), and was twice as great as theJ _d ^m of fructose. The apparent affinity constant,K _m ^* ,of glucose is less than that of fructose, which was lower than theK _m ^* of galactose and 3-O-MG. The use of the Lineweaver-Burk double reciprocal plot is associated with an overestimation of bothJ _d ^m andK _m ^* .This discrepancy between the true and apparent values of the kinetic constants is much greater for lower than for higher values ofJ _d ^m andK _m ^* ;variations in the resistance of the unstirred layer influences the magnitude and direction of the discrepancy. The apparent passive permeability coefficient is similar for each sugar, but because of the different values ofJ _d ^m , passive permeation contributes relatively more to the uptake of glucose and fructose than of galactose or 3-O-MG. Under conditions of high unstirred layer resistance, differences in uptake rates of the sugars are due to differences in theirJ _d ^m rather than theirK _m ^* .Kinetic analysis is compatible with the suggestion that the glucose carriers are predominantly near the tip of the villus, whereas those for galactose and 3-O-MG are located along the entire villus and theK _m ^* of their carriers at the tip is lower than theirK _m ^* towards the base of the villus. It is proposed that there are multiple or heterogeneous intestinal carriers for glucose, galactose and 3-O-methyl glucose in the jejunum of the rabbit.Abbreviations Used in this Paper C ₁ Concentration of the probe molecule in the bulk phase - C ₂ Concentration of the probe molecule at the aqueous-membrane interface - d Effective thickness of the intestinal unstirred water layer - D Free diffusion coefficient of the probe molecule     

Intestinal transport of weak electrolytes: Determinants of influx at the luminal surface

The determinants of weak electrolyte influx into everted segments of rat small intestine have been studied. Preliminary experiments showed that the observed influxes could be described as unidirectional, diffusional fluxes of the nonionized compound uncomplicated by a parallel ionic component. It is shown that the determinants of weak electrolyte influx in this situation may be described in terms of the resistance of the unstirred layer to movement from the bulk phase to the cell surface, the degree of ionization of the weak electrolyte at the cell surface, and the cellular permeability to the nonionized weak electrolyte. Quantitative considerations indicated that the unstirred layer was totally rate-limiting in the cases of some poorly ionized, or highly permeant compounds, but the unstirred layer was not totally rate limiting for most of the compounds studied. Calculation of cellular permeabilities for the nonionized forms of weak electrolytes required assumptions to be made concerning the pH value in the surface fluid layer. A uniform set of permeability data including both weak acids and weak bases was obtained only when it was assumed that the pH in the surface fluid layer was equal to that in the bulk phase, and it was concluded that these studies do not support the concept of a microclimate of distinctive pH at the epithelial surface as a determinant of weak electrolyte transport.     

Measurement of the effective thickness of the mucosal unstirred layer in Necturus gallbladder epithelium

The effective thickness of the unstirred fluid layer (USL) adjacent to an epithelial barrier can be estimated from the time course for the accumulation or depletion of a solute at the membrane surface. In 1985 we reported an unstirred layer thickness of approximately 70 microns for Necturus gallbladder epithelium. In our earlier studies the delay caused by noninstantaneous bulk solution mixing was not taken into account and thus the USL thickness was systematically overestimated. In the present studies we describe an analysis of the time course of solute arrival at the membrane surface that takes into account noninstantaneous bulk solution mixing. We also describe a simple technique to monitor the accumulation or depletion of a solute at the membrane surface. The time course for the change in the concentration of either tetramethylammonium (TMA+) or tetrabutylammonium (TBA+) upon elevation of bulk solution concentration is sensed at the membrane surface with an ion-sensitive microelectrode. Because of the high selectivity of the ion-sensitive resin for TMA+ or TBA+ over other monovalent cations in the solution (Na+ and K+), a low concentration (1-2 mM) of the probe can be used. By measuring the time course of the arrival of first one probe and then the other, under identical superfusion conditions, sufficient information is obtained to eliminate multiple fits to the data, obtained when only one probe is used. Neglecting bulk solution mixing caused an error greater than 50% in estimated apparent USL thickness. The effective thickness of the USL depends critically upon chamber geometry, flow rate, and the position of superfusion and suction pipettes. Under our experimental conditions the effective USL at the mucosal surface of Necturus gallbladder epithelium was approximately 40 microns.     

The permeability coefficient of the wall of a villous membrane

Summary The equations hitherto used to correct the permeability coefficient for the unstirred layer influence are valid only for flat membranes. Therefore, appropriate equations for membranes with a villous surface (e.g., small intestine) have been derived. They take into account the non-linear concentration gradient in the intervillous part of the unstirred layer. Quantitative information about the geometry of the villous surface and the unstirred layer thickness are needed to calculate the permeability coefficient of the membrane wall (e.g., intestinal epithelium). The concentration of highly permeable substances drops sharply already in the upper part of the intervillous space, so that the tips of the villi function as effective absorbing area. The intervillous concentration gradient of a substance with a low permeability coefficient is so small, that such a substance is absorbed by the total surface area of the villous membrane. The effective absorbing area of substances with intermediate permeability coefficient lies between the described limits.     

Measurement of diffusion within the cell wall in living roots of Arabidopsis thaliana

To quantify the diffusion constant of small molecules in the plant cell wall, fluorescence from carboxyfluorescein (CF) in the intact roots of Arabidopsis thaliana was recorded. Roots were immersed in a solution of the fluorescent dye and viewed through a confocal fluorescence microscope. These roots are sufficiently transparent that much of the apoplast can be imaged. The diffusion coefficient, D(cw), of CF in the cell wall was probed using two protocols: fluorescence recovery after photobleaching and fluorescence loss following perfusion with dye-free solution. Diffusion coefficients were obtained from the kinetics of the fluorescent transients and modelling apoplast geometry. Apoplastic diffusion constants varied spatially in the root. In the elongation zone and mature cortex, D(cw)=(3.2+/-1.4)x10(-11) m(2) s(-1), whereas in mature epidermis, D(cw)=(2.5+/-0.7)x10(-12) m(2) s(-1), at least an order of magnitude lower. Relative to the diffusion coefficient of CF in water, these represent reductions by approximately 1/15 and 1/195, respectively. The low value for mature epidermis is correlated with a suberin-like permeability barrier that was detected with either autofluorescence or berberine staining. This study provides a quantitative estimate of the permeability of plant cell walls to small organic acids-a class of compounds that includes auxin and other plant hormones. These measurements constrain models of solute transport, and are important for quantitative models of hormone signalling during plant growth and development.     

Oral Delivery of Lipophilic Drugs: The Tradeoff between Solubility Increase and Permeability Decrease When Using Cyclodextrin-Based Formulations

The purpose of this study was to investigate the impact of oral cyclodextrin-based formulation on both the apparent solubility and intestinal permeability of lipophilic drugs. The apparent solubility of the lipophilic drug dexamethasone was measured in the presence of various HPβCD levels. The drug’s permeability was measured in the absence vs. presence of HPβCD in the rat intestinal perfusion model, and across Caco-2 cell monolayers. The role of the unstirred water layer (UWL) in dexamethasone’s absorption was studied, and a simplified mass-transport analysis was developed to describe the solubility-permeability interplay. The PAMPA permeability of dexamethasone was measured in the presence of various HPβCD levels, and the correlation with the theoretical predictions was evaluated. While the solubility of dexamethasone was greatly enhanced by the presence of HPβCD (K_1∶1 = 2311 M⁻¹), all experimental models showed that the drug’s permeability was significantly reduced following the cyclodextrin complexation. The UWL was found to have no impact on the absorption of dexamethasone. A mass transport analysis was employed to describe the solubility-permeability interplay. The model enabled excellent quantitative prediction of dexamethasone’s permeability as a function of the HPβCD level. This work demonstrates that when using cyclodextrins in solubility-enabling formulations, a tradeoff exists between solubility increase and permeability decrease that must not be overlooked. This tradeoff was found to be independent of the unstirred water layer. The transport model presented here can aid in striking the appropriate solubility-permeability balance in order to achieve optimal overall absorption.     

Cellular energetics and the oxygen dependence of respiration in cardiac myocytes isolated from adult rat

The oxygen dependence of mitochondrial respiration was investigated using suspensions of mitochondria and quiescent ventricular myocytes isolated from adult rat hearts. A new optical method was used to determine oxygen concentration in the suspending media. The P50 for respiration for coupled mitochondria at a high [ATP]/[ADP].[Pi] ratio and oxidizing glutamate/malate was 0.45 +/- 0.03 microM but was increased to 0.57 +/- 0.02 microM by the addition of succinate to the substrate mixture. This value was decreased to less than 0.06 +/- 0.01 microM when the ATP/ADP.Pi ratio was decreased with the uncoupler, carbonyl cyanide p-trifluoromethoxyphenylhydrazone. The P50 value in resting myocytes was 2.23 +/- 0.13 microM at a Vmax of 13.22 +/- 1.38 nmol of O2/g, dry weight/min. During resting conditions, the creatine phosphate/creatine and ATPfree/ADPfree ratios were high in these cells, 6.81 +/- 1.11 and 1131 +/- 185, respectively. Addition of 1 mM Ca2+ to the suspending media increased the P50 by 50% whereas respiration rose by only 10%. Respiratory rate was increased up to about 10-fold by uncoupling the cells, but the P50 increased by less than 3-fold. When these uncoupled cells were inhibited with Amytal to lower the rate of oxygen consumption to that of resting cells, the P50 fell to 1.25 +/- 0.14 microM. Diffusion models indicate that in resting myocytes, the oxygen concentration difference from sarcolemma to cell core was approximately 1.84 microM with an additional difference of about 0.27 microM attributed to the unstirred layer of media surrounding each cell. The intracellular oxygen diffusivity coefficient in myocytes was calculated to be 0.30 x 10(-5) cm2/s. The results show that the oxygen dependence of respiration is modulated by the cellular metabolic state. At near maximal levels of respiration or on recovery from hypoxic episodes, oxygen diffusion may become an important determinant of the oxygen dependence of myocardial respiration.