Hypotonic hemolysis of human red blood cells: a two-phase process

Summary Previous use of hemolysis time measurement to determine permeability coefficients for the red blood cell membrane rested on the assumption that cells swelling in a hypotonic medium hemolyzed immediately on reaching critical volume. By preswelling red cells to various volumes prior to immersion in hemolytic solutions we extrapolate to the hemolysis time of red cells immersed at critical volume and thereby find a significant period of time during which the cells apparently remain in a spherical form prior to release of hemoglobin. Revised estimates of permeability coefficients follow from including this spherical (nonswelling) phase. In addition, the appreciation of a characteristic time period during which the membrane is under tension provides new opportunity to study physical and chemical properties of the membrane.Presented in part at the 1974 joint meeting of the Biophysical Society and the American Society of Biological Chemists.     

Shape and Volume Changes in Frog Erythrocytes Following Ultraviolet Radiation

Frog erythrocytes in Ringer's solution were exposed to ultraviolet radiation and then followed in camera lucida drawings for changes in shape and dimension. Cell thickness was found to increase while cell width remained constant throughout the period prior to hemolysis. The cell shortened and bulged at the ends during the middle third of the prolytic period while a region around the cell center remained constricted. When this constricted region gave way, the cell became spherical and hemolyzed. Cell volume as calculated from the cell's dimensions increased linearly with time throughout the prolytic period to hemolysis then dropped rapidly to a constant value somewhat higher than the original cell volume. These changes in shape and volume are consistent with a colloid osmotic type of hemolysis but with other factors acting to limit the rate of swelling and the forms assumed during the swelling process. The relationship between the time of hemolysis and the cell surface area exposed to the ultraviolet is discussed as it applies to the site of ultraviolet damage.     

Electrical hemolysis of human and bovine red blood cells.

The external electric field strength required for electrical hemolysis of human red blood cells depends sensitively on the composition of the external medium. In isotonic NaCl und KCl solutions the onset of electrical hemolysis is observed at 4 kV per cm and 50 per cent hemolysis at 6 kV per cm, whereas increasing concentrations of phosphate, sulphate, sucrose, inulin and EDTA shift the onset and the 50 per cent hemolysis-value to higher field strengths. The most pronounced effect is observed for inulin and EDTA. In the presence of these substances the threshold value of the electric field strength is shifted to 14 kV per cm. This is in contrast to the dielectric breakdown voltage of human red blood cells which is unaltered by these substances and was measured to be approximately 1 V corresponding in the electrolytical discharge chamber to an external electric field strength of 2 to 3 kV per cm. On the other hand, dielectric breakdown of bovine red blood cell membranes occurs in NaCl solution at 4 to 5 kV per cm and is coupled directly with hemoglobin release. The electrical hemolysis of cells of this species is unaffected by the above substances with exception of inulin. Inulin suppressed the electrical hemolysis up to 15 kV per cm. The data can be explained by the assumption that the reflection coefficients of the membranes of these two species to bivalent anions and uncharged molecules are field-dependent to a different extent. This explanation implies that electrical hemolysis is a secondary process of osmotic nature induced by the reversible permeability change of the membrane (dielectric breakdown) in response to an electric field. This view is supported by the observation that the mean volumes of ghost cells obtained by electrical hemolysis can be changed by changing the external phosphate concentration during hemolysis and resealing, or by subjecting the cells to a transient osmotic stress immediately after the electrical hemolysis step. An interesting finding is that the breakdown voltage, although constant throughout each normally distributed ghost size distribution, increases with increasing mean volume of the ghost populations.     

Alkaline hemolysis fragility is dependent on cell shape: results from a morphology tracker.

BACKGROUND: The morphometric analysis of red blood cells (RBCs) is an important area of study and has been performed previously for fixed samples. We present a novel method for the analysis of morphologic changes of live erythrocytes as a function of time. We use this method to extract information on alkaline hemolysis fragility. Many other toxins lyse cells by membrane poration, which has been studied by averaging over cell populations. However, no quantitative data are available for changes in the morphology of individual cells during membrane poration-driven hemolysis or for the relation between cell shape and fragility. METHODS: Hydroxide, a porating agent, was generated in a microfluidic enclosure containing RBCs in suspension. Automatic cell recognition, tracking, and morphometric measurements were done by using a custom image analysis program. Cell area and circular shape factor (CSF) were measured over time for individual cells. Implementations were developed in MATLAB and on Kestrel, a parallel computer that affords higher speed that approaches real-time processing. RESULTS: The average CSF went through a first period of fast increase, corresponding to the conversion of discocytes to spherocytes under internal osmotic pressure, followed by another period of slow increase until the fast lysis event. For individual cells, the initial CSF was shown to be inversely correlated to cell lifetime (linear regression factor R=0.44), with discocytes surviving longer than spherocytes. The inflated cell surface area to volume ratio was also inversely correlated to lifetime (R=0.43) but not correlated to the CSF. Lifetime correlated best to the ratio of cell inflation volume (Vfinal-Vinitial) to surface area (R=0.65). CONCLUSIONS: RBCs inflate at a rate proportional to their surface area, in agreement with a constant flux model, and lyse after attaining a spherical morphology. Spherical RBCs display increased alkaline hemolysis fragility (shorter lifetimes), providing an explanation for the increased osmotic fragility of RBCs from patients who have spherocytosis.     

Impact of blood manufacturing and donor characteristics on membrane water permeability and in vitro quality parameters during hypothermic storage of red blood cells

Several factors have been proposed to influence the red blood cell storage lesion including storage duration, blood component manufacturing methodology, and donor characteristics [1,18]. The objectives of this study were to determine the impact of manufacturing method and donor characteristics on water permeability and membrane quality parameters.Red blood cell units were obtained from volunteer blood donors and grouped according to the manufacturing method and donor characteristics of sex and age. Membrane water permeability and membrane quality parameters, including deformability, hemolysis, osmotic fragility, hematologic indices, supernatant potassium, and supernatant sodium, were determined on day 5 ± 2, day 21, and day 42. Regression analysis was applied to evaluate the contribution of storage duration, manufacturing method, and donor characteristics on storage lesion.This study found that units processed using a whole blood filtration manufacturing method exhibited significantly higher membrane water permeability throughout storage compared to units manufactured using red cell filtration. Additionally, significant differences in hemolysis, supernatant potassium, and supernatant sodium were seen between manufacturing methods, however there were no significance differences between donor age and sex groups.Findings of this study suggest that the membrane-related storage lesion is initiated prior to the first day of storage with contributions by both blood manufacturing process and donor variability. The findings of this work highlight the importance of characterizing membrane water permeability during storage as it can be a predictor of the biophysical and chemical changes that affect the quality of stored red blood cells during hypothermic storage.     

Electrical hemolysis of human and bovine red blood cells

Summary The external electric field strength required for electrical hemolysis of human red blood cells depends sensitively on the composition of the external medium. In isotonic NaCl und KCl solutions the onset of electrical hemolysis is observed at 4 kV per cm and 50% hemolysis at 6 kV per cm, whereas increasing concentrations of phosphate, sulphate, sucrose, inulin and EDTA shift the onset and the 50% hemolysis-value to higher field strengths. The most pronounced effect is observed for inulin and EDTA. In the presence of these substances the threshold value of the electric field strength is shifted to 14 kV per cm. This is in contrast to the dielectric breakdown voltage of human red blood cells which is unaltered by these substances and was measured to be 1 V corresponding in the electrolytical discharge chamber to an external electric field strength of 2 to 3 kV per cm. On the other hand, dielectric breakdown of bovine red blood cell membranes occurs in NaCl solution at 4 to 5 kV per cm and is coupled directly with hemoglobin release. The electrical hemolysis of cells of this species is unaffected by the above substances with exception of inulin. Inulin suppressed the electrical hemolysis up to 15 kV per cm. The data can be explained by the assumption that the reflection coefficients of the membranes of these two species to bivalent anions and uncharged molecules are field-dependent to a different extent. This explanation implies that electrical hemolysis is a secondary process of osmotic nature induced by the reversible permeability change of the membrane (dielectric breakdown) in response to an electric field. This view is supported by the observation that the mean volumes of ghost cells obtained by electrical hemolysis can be changed by changing the external phosphate concentration during hemolysis and resealing, or by subjecting the cells to a transient osmotic stress immediately after the electrical hemolysis step. An interesting finding is that the breakdown voltage, although constant throughout each normally distributed ghost size distribution, increases with increasing mean volume of the ghost populations.     

Effects of low electrolyte media on salt loss and hemolysis of mammalian red blood cells.

Cation loss and hemolysis of various mammalian red cells suspended in isotonic non-electrolyte media were investigated. Sucrose buffered with 10 mM Tris-Hepes, pH 7.4 was used as the non-permeable non-electrolyte. Mammals from which the red cells were derived include the human, guinea pig, rat, rabbit, newborn calf, newborn piglet and pig, all of which contain K as the predominant cation species (HK type) and the dog, cat, sheep and cow, all of which possess Na as the predominant cation species (LK type). Of HK cells, a rapid efflux of K takes place from humans, rats and guinea pigs. Of LK type cells, the dog and cat exhibit an augmented membrane permeability to Na. The governing factors which influence cation permeability are the change in pH, temperature, and ionic strength. In response to increase in pH, the red cells of humans, dogs and cats become more permeable to cations, whereas the red cells of rat and rabbit are unaffected. In response to increase in temperature, HK type cells exhibit augmented K efflux, while the Na loss from the dog and cat cells manifest a well-defined maximum at near 37 degrees C. In all cases, a small substitution of sucrose by an equal number of osmoles of salts results in a dramatic decrease in cation loss. By contrast, the red cells of the rabbit, newborn calf, adult cow, newborn piglet, adult pig and sheep display no discernible increase in ion-permeability under the conditions alluded to above. In some species including the newborn calf, dog, and cat, an extensive hemolysis occurs usually within an hour in isotonic buffered sucrose solution. The osmolarity of sucrose solution affects these cells differently in that as the osmolarity increases from 200--500 mM, hemolytic rates of the calf and dog reach a saturation near 300 mM sucrose, whereas the hemolytic rate of the cat decreases progressively. Common features pertaining to this hemolysis are (1) the intracellular alkalinization process; and (2) the diminution of the cell volume which take place prior to and onset of hemolysis. SITS, a potent anion transport inhibitor, completely protects the cells from hemolysis by inhibiting chloride flux and the concomitant rise in intracellular pH.     

The relationship of membrane lipids to species specific hemolysis by hemolytic factors from Stomoxys calcitrans (L.) (Diptera: Muscidae)

Posterior-midgut homogenate from female stable flies prepared at 12 h after feeding hemolyzed erythrocytes from 6 different mammalian species more readily than homogenate prepared at 22 h. A significant correlation was obtained between the per cent sphingomyelin content of the erythrocyte membrane and the time required for lysis by the 12 h homogenate. Erythrocytes with low sphingomyelin content were more sensitive to lysis than cells with high sphingomyelin. No such correlation exists for hemolysis by 22 h homogenate. Mean corpuscular volume and osmotic fragilities of erythrocytes were not related to hemolysis either by 12 or 22 h homogenate. Determination of phospholipase C and sphingomyelinase activities showed that the hydrolysis rate of phospholipase C in homogenates prepared at 12–14 h was almost twice as much as sphingomyelinase activity. Whereas hydrolysis rates in 22–24 h homogenate were not different and markedly reduced compared to the 12–14 h homogenate. The times required for erythrocyte hemolysis related to the phospholipase C and sphingomyelinase activity profiles suggests that these enzyme activities participate in the in vitro hemolysis of red blood cells. Bovine and human erythrocytes change their biconcave contour into a spiculated spherical shape when they are exposed to midgut homogenate. This shape change is interpreted as a detergent induced modification of the red cell membrane which renders the erythrocytes more vulnerable to hemolysis.     

The permeability of human cells to cations after treatment with resorcinol,n-butyl alcohol,and similar lysins

The form of families of curves relating K loss to time in systems containing hypolytic concentrations of resorcinol and of n-butyl alcohol points to the human red cell's being slightly permeable to K and Na even when it is in isotonic NaCl (or plasma), and to the effect of the hypolytic concentrations of lysin being such as to increase this permeability. The rate of reentry of K into red cells which have lost it is more rapid than the rate of the previous loss. This may be due to the reimmersion of the lysin-treated cells in isotonic KCl producing further modifications of the ion-restricting mechanisms associated with the red cell structure. The volume changes observed in systems which show the large K-Na exchanges produced by resorcinol and by n-butyl alcohol are not the same as those which would be expected on the basis of the dual mechanism of hemolysis hypothesis or of the colloid-osmotic hemolysis hypothesis. Extensive swelling of the red cells occurs only when the concentrations of lysin are large enough to produce considerable hemolysis.     

Sugar transport in reversibly hemolyzed avian erythrocytes.

The technique of reversible hemolysis represents one approach which may be used to study transport regulation in nucleated red cells. After 1 h of incubation at 37 degrees C, 88% of the ghosts regained their permeability barrier to L-glucose. In these ghosts, the carrier-mediated rate of entry of 3-O-methylglucose was more than 10-fold greater than the rate in intact cells. Glyceraldehyde-3-phosphate dehydrogenase prevented ghosts from resealing when it was present at the time of hemolysis. Albumin, lactic dehydrogenase and peroxidase did not have this effect. Sugar transport rate could not be tested in the unsealed ghosts. Two possible mechanisms for the effect of hypotonic hemolysis on sugar transport rate were discussed: (1) altered membrane organization and (2) loss of intracellular compounds which bind to the membrane and inhibit transport in intact cells.     

Transitory postnatal hemolysis of calf red cells by amino acids

Summary Among the amino acids which can be solubilized to give a concentration of 300 mM at near physiological pH, histidine and proline caused a complete hemolysis of newborn calf but not of adult cow red cells within 20 to 30 minutes at 38°C. While hydroxyproline, valine, and serine resulted in a partial lysis of calf cells, threonine, glutamine, and glycine were inefective. In this communication, emphasis has been focused on the mode of the lytic process by histidine, which was found to be affected by several governing parameters including the pH, temperature and the extracellular salts in the solution. Unlike human red cells suspended in isotonic histidine, both calf and cow cells lost little Na and K ions. In the presence of 300 mM histidine, both calf and cow cells displayed an instantaneous uptake of histidine amounting to 20 to 45 moles/ml RBC followed by a slow influx rate of 0.25 to 0.5 moles/ml RBC×min. The extent to which histidine entry was allowed by the cell was counterbalanced by Cl^– efflux, resulting in little change in cell volume prior to hemolysis. Moreover, histidine-induced hemolysis can by prevented by 1 mM or lower PCMBS without at discernible effect on histidine influx suggesting a possible membrane lesion or damage at the outer surface of the cell.Hemolysis induced by histidine decreased substantially when a calf reached two months of age which time the red cells containing the fetal hemoglobin are virtually depleted. The results of hemoglobin electroiphoresis obtained during this postnatal period revealed that those cells resistant to histidine hemolysis almost invariably contain the adult type hemoglobin suggesting a selective, speicific action of the amin acid on the featal cells.A preliminary report of these data has been presented at the 19th Annual Meeting (1975) of the Biophysical Society, Philadelphia, Pennsylvania.     

Hemolysis of human red blood cells by freezing and thawing in solutions containing sucrose: relationship with posthypertonic hemolysis and solute movements

Human red blood cells were frozen at temperatures down to ?9 °C in solutions containing sucrose, and the hemolysis on thawing was measured. This was compared with the hemolysis caused by exposing the cells to high concentrations of sucrose and then resuspending them in more dilute solutions at 4 °C. The effects of the hypertonic solutions of sucrose on potassium, sodium, and sucrose movements were also investigated. It was found that sucrose does not prevent damage to the cells by very hypertonic solutions (whether during freezing and thawing or at 4 °C) but it does reduce hemolysis of cells previously exposed to these solutions if present in the resuspension (or thawing) solution. Evidence is presented that the damaging effects of the hypertonic solutions of sucrose occurring during freezing are associated with changes in cell membrane permeability but that posthypertonic hemolysis is not primarily associated with a “loading” of the cells with extracellular solutes in the hypertonic phase. It is concluded that sucrose may reduce hemolysis of red blood cells by slow freezing and thawing by reducing colloid osmotic swelling of cells with abnormally permeable membranes.     

Abnormalities of elastic and transporting properties of red blood cells under development of apoptosis

The functional properties of erythrocytes under development of apoptotic process in these cells were investigated by the low angle light scattering technique. Apoptosis induced by ionomycin was associated with an initial decrease of cell volume and caused formation of echinocytes. After that the cells restored their volume forming rounded erythrocytes with rugged membrane capable to agglomerate with each other. At the late stages of apoptosis, small fragmented cells can be revealed. Preapoptotic red blood cells (at all stages of apoptosis) manifested an enormous tolerance to hypotonic loading, whereas control cells hemolyzed just after reaching a critical volume (∼150 fl). Acidic hemolysis cannot differentiate between control and preapoptotic erythrocytes, the cells being hemolyzed not reaching the critical volume. Placing the control erythrocytes to a medium with ammonia ions instead of sodium ions caused an initial increase of cell volume above the critical point, and then it was also followed by hemolysis. Under ammonia loading, an initial rate of the cell volume growth and a ratio of the hemolyzed cells were significantly reduced in preapoptotic cells.     

Hemolysis of human red blood cells by freezing and thawing in solutions containing polyvinylpyrrolidone: relationship with postthypertonic hemolysis and solute movements

An investigation was made into the effects of the presence of polyvinylpyrrolidone (PVP) on changes in human red blood cells suspended in hypertonic solutions, on posthypertonic hemolysis, and on freezing at temperatures down to ?12 °C.PVP is very effective at reducing hemolysis when the red blood cells are frozen at temperatures down to ?12 °C. However, the membranes of the cells recovered on thawing have become very permeable to sodium and potassium ions and there is a much increased hemolysis if the cells are resuspended in an isotonic solution of sodium chloride.The presence of PVP does not affect the dehydration of the cells or the development of a change in membrane permeability when the cells are shrunken in hypertonic solutions at 0 °C. Neither does its presence in the hypertonic solution reduce the extent of posthypertonic hemolysis at 4 °C (as measured by the hemolysis on resuspension in an isotonic solution of sodium chloride), but it is more effective than sucrose at reducing hemolysis when present in the resuspension solution. It is concluded that the PVP is able to prevent swelling and hemolysis of cells which are very permeable to cations by opposing the colloid osmotic pressure due to the hemoglobin. However, this does not explain how PVP is able to protect cells against freezing damage at high cooling rates, and a mechanism by which it might do this is discussed.     

Proteolytic activity of human erythrocyte membrane during ghosts preparation

1. Proteins in human erythrocyte membranes after red blood cells hemolysis revealed relatively high rate of self-digestion. 2. This indicates hemolysis as a critical moment for membrane proteases activation. 3. The detailed pattern of band 3 protein and spectrin degradation during ghosts preparation was more complicated and reflected both the changes in proteolytic susceptibility and extraction of some proteases. 4. Further extraction of membrane proteins by alkali stripping resulted in an increase in the self-digestion rate and decrease in the degradation rate of an exogenous substrate.     

Sugar transport in reversibly hemolyzed avian erythrocytes

The technique of reversible hemolysis represents one approach which may be used to study transport regulation in nucleated red cells. After 1 h of incubation at 37°C, 88% of the ghosts regained their permeability barrier to l-glucose. In these ghosts, the carrier-mediated rate of entry of $\text{3-O-}\text{methylglucose}$ was more than 10-fold greater than the rate in intact cells. Glyceraldehyde-3-phosphate dehydrogenase prevented ghosts from resealing when it was present at the time of hemolysis. Albumin, lactic dehydrogenase and peroxidase did not have this effect. Sugar transport rate could not be tested in the unsealed ghosts. Two possible mechanisms for the effect of hypotonic hemolysis on sugar transport rate were discussed: (1) altered membrane organization and (2) loss of intracellular compounds which bind to the membrane and inhibit transport in intact cells.     

A simple method for determination of red blood cell mechanical fragility in the rat

A method for measuring the mechanical fragility of red blood cells suitable for use in small laboratory animals, such as rats, is reported because of lack of such data in the literature. Whole blood is mixed with phosphate buffered saline in a tube containing glass beads. The tubes are rocked for 90 minutes, centrifuged and the percent hemolysis determined. Varying the osmolality of the saline suspending medium had little effect on the mechanical fragility of rat red cells prior to the NaCl concentrations at which a significant change in osmotic hemolysis occurred. The duration of rocking increased the mechanical fragility. Varying the pH (6.4-8.0) had no effect. The size of the glass beads changed the mechanical fragility as did varying temperature. The mean mechanical fragility of rat red blood cells was 46% hemolysis (80 adult male animals). Because of the small volume of blood required with this method, mechanical fragility of red cells of other small laboratory animals also may be determined.     

Studies on the cation permeability of human red cell ghosts. Characterization and biological significance of two membrane sites with high affinities for Ca.

Net K movements in reconstituted human red cell ghosts and the resealing of ghosts to cations after osmotic hemolysis of red cells have been studied as functions of the free Ca ion concentration. The Ca-dependent specific increase in K permeability was shown to be mediated by a site close to the internal surface of the membrane with an apparent dissociation constant ap pH 7.2 for Ca (K'p1) of 3-5 X 10(-7) M, for Sr of 7 X 10(-6) M. Ba and Mg did not increase the K-permeability of the membrane but inhibited the Ca-mediated permeability changes. K'D1 decreased in a nonlinear fashion when the pH was increased from 6.0 to 8.5. Two different pK' values of this membrane site were found at pH 8.3 and 6.3. The Ca-activated net K efflux into a K-free medium was almost completely inhibited by an increase in intracellular Na from 4 to 70mM. Extracellular K antagonized this Na effect. Changes in the extracellular Na (0.1-140 mM) or K (0.1-6 mM) concentrations had little effect and did not change K'p1. The Ca-stimulated recovery of a low cation permeability in ghost cells appeared to be mediated by a second membrane site which was accessible to divalent cations only during the process of hemolysis in media of low ionic strength. The apparent dissociation constant for Ca at this site (K'p2) varied between 6 X 10(-7) and 4 X 10(-6) M at pH 7.2 Mg, Sr, and Ba could replace Ca functionally. The selectivity sequence was Ca greater than Sr greater than Ba greater than Mg. K'p2 was independent on the pH value in the range between 6.0 and 8.0 Hill coefficients of 2 were observed for the interaction of Ca with both membrane sites suggesting that more than one Ca ion is bound per site. The Hill cofficients were affected neither by the ion composition nor by the Ph values of the intra-and extracellular media. It is concluded that two different pathways for the permeation of cations across the membrane are controlled by membrane sites with high affinities for Ca: One specific for K, one unspecific with respect to cations. The K-specific "channel" has properties similar to the K channel in excitable tissues.     

Effect of hexachlorophene on monovalent cation transport in human erythrocytes a mechanism for hexachlorophene-induced hemolysis

Hexachlorophene-induced hemolysis, as studied by phase contrast microscopy, appeared to be a result of osmotic swelling. Both swelling and subsequent hemolysis were markedly delayed by addition of the non-penetrating solute sucrose to the incubation mixture. Binding studies indicated that hexachlorophene is associated primarily with the erythrocyte membrane, the remainder being found in the cytoplasm. Hexachlorophane induced a dose-dependent, first-order efflux of Na⁺ and K⁺ from red cells. The rates of hemolysis and K⁺ efflux induced by hexachlorophene were much greater than would be expected if this compound were acting simply as a metabolic inhibitor and/or an inhibitor of (Na⁺-K⁺-Mg²⁺)-ATPase. It is suggested that hexachlorophene induces the efflux of Na⁺ and K⁺ from red cells by directly altering the permeability of the cellular membrane. Further, hexachlorophene-induced hemolysis is probably a secondary event resulting from osmotic swelling subsequent to increased membrane permeability.     

Red Cell Membrane Permeability Deduced from Bulk Diffusion Coefficients

The permeability coefficients of dog red cell membrane to tritiated water and to a series of[¹⁴C]amides have been deduced from bulk diffusion measurements through a "tissue" composed of packed red cells. Red cells were packed by centrifugation inside polyethylene tubing. The red cell column was pulsed at one end with radiolabeled solute and diffusion was allowed to proceed for several hours. The distribution of radioactivity along the red cell column was measured by sequential slicing and counting, and the diffusion coefficient was determined by a simple plotting technique, assuming a one-dimensional diffusional model. In order to derive the red cell membrane permeability coefficient from the bulk diffusion coefficient, the red cells were assumed to be packed in a regular manner approximating closely spaced parallelopipeds. The local steady-state diffusional flux was idealized as a one-dimensional intracellular pathway in parallel with a one-dimensional extracellular pathway with solute exchange occurring within the series pathway and between the pathways. The diffusion coefficients in the intracellular and extracellular pathways were estimated from bulk diffusion measurements through concentrated hemoglobin solutions and plasma, respectively; while the volume of the extracellular pathway was determined using radiolabeled sucrose. The membrane permeability coefficients were in satisfactory agreement with the data of Sha'afi, R. I., C. M. Gary-Bobo, and A. K. Solomon (1971. J. Gen. Physiol. 58:238) obtained by a rapid-reaction technique. The method is simple and particularly well suited for rapidly permeating solutes.