Analysis of the Components of Ionic Flux across a Membrane

The unidirectional flux of an ionic species may occur because of several mechanisms such as active transport, passive diffusion, exchange diffusion, etc. The contribution of such mechanisms to the total unidirectional flux across a membrane cannot be determined by only measuring that flux. It is shown that if the pertinent experimental data (the opposite unidirectional fluxes and the composite phenomenological resistance coefficient of the ionic species for a given electrochemical potential difference) obey a certain inequality, then the parameters of a model consisting of parallel, independent, active transport, and passive processes may be determined. Although the existence of "additional" processes including exchange diffusion, single-file pore diffusion, isotope interaction, etc. is not disproved, their existence is unnecessary if the inequality is satisfied. Two types of violations of the inequality may occur: (a) if the upper limit is disobeyed the presence of another substance contributing to the measured resistance and/or a constant affinity of the active transport process may be indicated; (b) if the lower limit is disobeyed it is necessary to postulate the existence of an additional process. For the latter type of violation, exchange diffusion is chosen as an example. Methods are given for determining the contribution of exchange diffusion, active transport, and passive diffusion to the unidirectional flux for some special cases.     

Single-file diffusion of uncharged particles

An equation for unidirectional fluxes of nonelectrolytes and for the total flux in the single-file transport through a narrow pore has been derived. The equation obtained accounts for the correlations of the population of the pore in the coordinate of transport. The problem has been solved using superposition approximation and unidirectional fluxes has been found. The population profile in the pore was shown to have nonlinear shape; this is principally different from the results of the classical diffusion approach.     

Analysis of models of single-file diffusion

Theoretical models of single-file transport in a homogeneous channel are considered. Three levels of channel populations were specified for which different approximations could be used. The results of these approximations are in good agreement with the results of a computer experiment (Aityan and Portnov 1986). At low populations, the pair correlation functions were negligibly small and allowed the use of linear approximation for unidirectional fluxes and populations. The value of the pair correlation function and the respective approximation for fluxes was obtained by the two-particles random-walk technique. At extremely high populations, the "divider" technique was proposed to describe the single-file transport. The divider technique allowed to explain the exponential shape of the pair correlation function FABn, n + 1 profile at extremely high populations. At medium populations the finite difference superposition approximation was valid.     

The flux ratio equation under nonstationary conditions

Summary The time dependent (i.e., nonstationary) unidirectional fluxes through a multilayered system consisting of sandwiched layers of arbitrary composition and exhibiting arbitrary potential and resistance profiles have been calculated, assuming that the flux is governed by the Smoluchowski equation (i.e., a flux resulting from a diffusion process superimposed upon a migration and/or a convection process, where part of the latter may arise from an active transport process). It is shown that during the building up of the concentration profile of the isotope inside the system towards the stationary value the ratio between the two oppositely directed, time-dependent unidirectional fluxes is, from the very first appearance of the isotope in the surrounding solutions, equal to the value of the stationary flux ratio. The practical implications of this result are discussed.     

Single-file diffusion through K+ channels in frog skin epithelium

Summary The ratio between the unidirectional fluxes of K⁺ across the frog skin with K-permeable outer membranes was determined in the absence of Na⁺ in the apical solutions. The experiments were performed under presteady-state conditions to be able to separate the flux ratio for K⁺ through the cells from contributions to the fluxes through extracellular leaks. The cellular flux ratio deviated strongly from the value calculated from the flux ratio for electrodiffusion. The experiments can be explained if the passive K transport through the epithelial cells proceeds through specific channels by single-file diffusion with a flux ratio exponent of about 2.5.     

Anion transport across the red blood cell membrane mediated by dielectric pores

Summary The anion transport across the red blood cell membrane is assumed to occur by ionic diffusion through dielectric pores which are formed by protein molecules spanning the red blood cell membrane. The access of anions to the dielectric pores is regulated by anion adsorption sites positioned at the entrances of the pores. The adsorption of small inorganic anions to the adsorption sites is facilitated by ionizing cationic groups setting up a surface potential at the respective membrane surfaces. Applying the transition state theory of rate processes, flux equations for the unidirectional flux were derived expressing the unidirectional flux as a function of the fractional occupancies of anion adsorption sites at both membrane surfaces.The basic properties of the transport model were investigated. The concentration-dependence and the pH-dependence of the unidirectional fluxes were shown to depend upon the surface charge density and upon the affinity of the transported anion species to the anion binding sites. The concentration-response and the pH-response of the unidirectional fluxes of different anion species may differ substantially even if the anion species are transported by the same anion transport system. The model predicts a characteristic behavior of the Lineweaver-Burk plot and of the Dixon plot.A comparison between computer simulated and experimentally determined flux curves was made. By choosing a suitable set of parameters, the anion transport model is capable of simulating the concentration-dependencies and the pH-dependencies of the unidirectional sulfate and chloride flux. It is sufficient to change one single constant in order to convert the sulfate transport system into a chloride transport system. Furthermore, the model is capable of predicting the inhibitory action of chloride on the sulfate transport system. No attempts were made to fit the experimental data to the model. The behavior of the model was qualitatively in accordance with the experimental results.     

Ionic transfer across the isolated frog large intestine

The unidirectional fluxes of sodium, chloride, and of the bicarbonate and CO(2) pair were determined across the isolated large intestine of the bullfrog, Rana catesbiana. The isolated large intestine of the frog is characterized by a mean transmembrane potential of 45 mv., serosal surface positive with respect to mucosal. The unidirectional sodium flux from mucosal to serosal surface was found to be equal to the short-circuit current, thus the net flux was less than the simultaneous short-circuit current. This discrepancy between active sodium transport and short-circuit current can be attributed to the active transport of cation in the same direction as sodium and/or the active transport of anion in the opposite direction. The unidirectional fluxes of chloride and the bicarbonate and CO(2) pair revealed no evidence for active transport of either anion. A quantitative study of chloride fluxes at 45 mv. revealed a flux ratio of 1.8 which is considerably less than a ratio of 6 expected for free passive diffusion. It was concluded that a considerable proportion of the isotopic transfer of chloride could be attributed to "exchange diffusion." Study of the electrical properties of the isolated frog colon reveals that it can be treated as a simple D. C. resistance over the range of -20 to +95 mv.     

Sodium fluxes through the active transport pathway in toad bladder.

To assess the active components of sodium flux across toad bladder as a function of transepithelial potential, unidirectional sodium fluxes between identical media were measured before and after adding sufficient ouabain (1.89 X 10(-3)M) to eliminate active transport, while clamping transepithelial potential to 0, 100 or 150 mV. Evidence was adduced that ouabain does not alter passive fluxes, and that fluxes remain constant if ouabain is not added. Hence, the ouabain-inhibitable fluxes represent fluxes through the active path. Results were analyzed by a set of equations, previously shown to describe adequately passive fluxes under electrical gradients in this tissue, here modified by the insertion of E, the potential at which bidirectional sodium fluxes (beta E, and theta E) through the active pathway are equal. According to these equations, beta E and theta E are the logarithmic mean of bidirectional fluxes through the active path at any potential, and the flux ratio in this path is modified by a constant factor Qia, which represents the ratio of the bulk diffusion coefficient to the tracer diffusion coefficient in this pathway. The data are shown to conform closely to these equations. Qia averages 2.54. Hence, serosal-to-mucosal flux vanishes rapidly as potential falls below E. Mean E in these experiments was 158 +/- 1 mV. Thus, linear dependence of net flux in both active and passive pathways on potential is present, even though the sodium fluxes in both paths fail to conform to the Ussing flux ratio equation. Qip less than 1 in the passive path (qualitatively similar to exchange diffusion) and Qia greater than 1 in the active path (as in single file pore diffusion). Both of these features tend to reduce the change in serosal-to-mucosal sodium flux induced by depolarization from spontaneous potential to zero potential ("short-circuiting").     

Unidirectional fluxes in saturated single-file pores of biological and artificial membranes I. Pores containing no more than one vacancy

A theoretical treatment of isotope fluxes in filled single-file pores is given. The treatment is confined to pores permitting only one vacancy at a time. Tracer flux, unidirectional fluxes and net flux are calculated. The exponent n which is obtained by representing the ratio of unidirectional fluxes as a power of the electrochemical activity-ratio proves to be closely related with m, the number of sites per pore. The minimum and maximum values of n are m?1 and m. It is shown that measurement of n provides sufficient information to determine m if the energetic properties of sites and barriers do not change too much with varying concentrations. Unlike the unidirectional fluxes, the net fluxes yield no direct information about the number of sites. The concentration dependence of the net fluxes, however, can be used to discriminate between the two limiting cases, n = m?1 and n = m. It is interesting with regard to the instantaneous potassium currents of nerve membranes that a suitable choice of the energetic parameters of a filled pore leads to a quasi-linearity of the net flux-voltage curves, which is only slightly affected by variation of the external concentration.     

Sodium fluxes through the active transport pathway in toad bladder

Summary To assess the active components of sodium flux across toad bladder as a function of transepithelial potential, unidirectional sodium fluxes between identical media were measured before and after adding sufficient ouabain (1.89×10^–3 m) to eliminate active transport, while clamping transepithelial potential to 0, 100 or 150 mV. Evidence was adduced that ouabain does not alter passive fluxes, and that fluxes remain constant if ouabain is not added. Hence, the ouabain-inhibitable fluxes represent fluxes through the active path. Results were analyzed by a set of equations, previously shown to describe adequately passive fluxes under electrical gradients in this tissue, here modified by the insertion ofE, the potential at which bidirectional sodium fluxes ( ^E and ^E ) through the active pathway are equal. According to these equations, ^E and ^E are the logarithmic mean of bidirectional fluxes through the active path at any potential, and the flux ratio in this path is modified by a constant factorQ _ia, which represents the ratio of the bulk diffusion coefficient to the tracer diffusion coefficient in this pathway. The data are shown to conform closely to these equations.Q _ia averages 2.54. Hence, serosal-to-mucosal flux vanishes rapidly as potential falls belowE. MeanE in these experiments was 158±1 mV. Thus, linear dependence of net flux in both active and passive pathways on potential is present, even though the sodium fluxes in both paths fail to conform to the Ussing flux ratio equation.Q _{i p}<1 in the passive path (qualitatively similar to exchange diffusion) andQ _ia>1 in the active path (as in single file pore diffusion). Both of these features tend to reduce the change in serosal-to-mucosal sodium flux induced by depolarization from spontaneous potential to zero potential (short-circuiting).     

Kinetic models and phenomenological analysis of passive lipid translocation in single-file

Passive movement of lipids through a membrane-embedded pore is analysed with kinetic equations of transport in single-file. The number of lipids arranged along the translocation coordinate in the pore is not limited in the calculations. The assumption is made that the energetic state of a pore is independent of the sequence of lipids contained in it. The results are valid for an arbitrary number of species with identical kinetic constants. It is shown that infinitely fast diffusion of one vacant site is equivalent to the filled pore approximation, which has been used here. We introduce the concept of non-strict single-file, which allows also for exchanges of neighbouring lipids inside the pore at specified rates. The model successfully simulates the redistribution of lipids between the monolayers of red blood cell plasma membranes under operation of an active aminophospholipid translocase. Kinetic equations are related to linear flux force relations. Phenomenological coefficients are expressed and analysed in terms of kinetic constants. Plausible kinetic pore model parameters are derived from comparison with a reference simulation of a thermodynamic model of the erythrocyte transmembrane lipid distribution. Mechanical forces due to differences in compressions of the lipid molecules between the monolayers are incorporated in kinetic rate constants. It is seen how the active inward transport of aminophospholipids causes an unsymmetrical passive redistribution of the other components due to mechanical effects and cross-coupling of fluxes.     

Transport of butyrate across the isolated bovine rumen epithelium--interaction with sodium, chloride and bicarbonate

The Ussing chamber technique was used for studying unidirectional fluxes of 14C-butyrate across the bovine rumen epithelium in vitro. Significant amounts of butyrate were absorbed across the bovine rumen epithelium in vitro, without any external driving force. The paracellular pathway was quantitatively insignificant. The transcellular pathway was predominately voltage-insensitive. The serosal to mucosal (SM) pathway was regulated by mass action, whereas the mucosal to serosal (MS) pathway further includes a saturable process, which accounted for 30 to 55% of the MS flux. The studied transport process for 14C-butyrate across the epithelium could include metabolic processes and transport of 14C-labelled butyrate metabolites. The transport of butyrate interacted with Na+, Cl- and HCO3-, and there was a linear relationship between butyrate and sodium net transport. Lowering the sodium concentration from 140 to 10 mmol l-1 decreased the butyrate MS flux significantly. Amiloride (1 mmol l-1) did, however, not reduce the butyrate flux significantly. Chloride concentration in itself did not seem to influence the transport of butyrate, but chloride-free conditions tended to increase the MS and SM flux of butyrate by a DIDS-sensitive pathway. DIDS (bilateral 0.5 mmol l-1) did further decrease the butyrate SM flux significantly at all chloride concentrations. Removing bicarbonate from the experimental solutions decreased the MS and increased the SM flux of butyrate significantly, and abolished net butyrate flux. There were no significant effects of the carbonic anhydrase inhibitor Acetazolamide (bilateral 1.0 mmol l-1). The results can be explained by a model where butyrate and butyrate metabolites are transported both by passive diffusion and by an electroneutral anion-exchange with bicarbonate. The model couples sodium and butyrate via CO2 from metabolism of butyrate, and intracellular pH.     

UPTAKE OF GLUCOSE ANALOGUES BY RAT BRAIN CORTEX SLICES: A KINETIC ANALYSIS BASED UPON A MODEL

Abstract— In slice preparations the exchange of dissolved substances between cells and incubation medium is delayed by diffusion through the extracellular space. The delay may seriously interfere with the study of membrane transport in terms of unidirectional fluxes across the cell membranes. A three-compartment serial model has been developed to describe exchange between slice and incubation medium. By aid of this model it is shown that the diffusion delay prevents determination of unidirectional fluxes for the two non-metabolizable glucose analogues 3-O-methylglucose and α-methyl-glucosidc. The membrane transport of the slowly transported α-methylglucoside can however be examined by aid of the model whereas the transport of 3-O-methylglucose is so rapid that it can not be examined with respect to V_max K_m and K_r. An attempt to determine these parameters will result in falsely large values which reflect extracellular diffusion and not membrane transport.     

Permeability of the human red blood cell tomeso-erythritol

Summary Using¹⁴C-erythritol, we measured net as well as unidirectional erythritol fluxes. Up to near saturation, net and unidirectional fluxes were virtually identical and linearly related to the erythritol concentration in the medium (isotonic saline). No saturation of the transfer system was observed. At 20°C, a maximum of 60 to 70% of the erythritol flux could be inhibited by glucose, phlorizin, or a combination of both substances. Dinitrofluorobenzene and HgCl₂ also reduce erythritol permeability. These findings confirm the earlier conclusion of F. Bowyer and W. F. Widdas that the glucose transport system is involved in erythritol permeation. Glycerol partially inhibits the glucose-phlorizin-sensitive component of erythritol flux, but not the glucose-phlorizin-insensitive component. Apparently glycerol has a slight affinity to that portion of the glucose transport system which is involved in erythritol transfer, whereas the glucosephlorizin-insensitive fraction of erythritol movements is not identical with the glycerol system. This latter inference is supported by the observation that, in contrast to glycerol permeability, erythritol permeability is insensitive to variations of pH or to the addition of copper. The apparent activation energy of the glucose-phlorizin-sensitive and-insensitive fractions of erythritol permeation are 22.2 and 20.7 kcal/mole, respectively. These values are not significantly different from one another.     

Sodium Fluxes in the Erythrocytes of Swine, Ox, and Dog

Sodium fluxes were measured in erythrocytes from three species of mammals. Unidirectional fluxes were slowest in swine RBCs (low sodium cells), fastest in dog RBCs (high sodium cells), and between these extremes in ox cells (intermediate level of internal sodium). In addition, efflux and influx in swine cells both correlated positively with intracellular sodium concentration between 12 to 4 µeq/ml. Tracer effluxes in swine and beef cells were separated into three components: active transport, diffusion, and exchange diffusion. The last two also contributed to influx. Transport was greater in swine cells than in beef, while the leak was similar in both. Pump to leak ratios were about 21 for swine and 3 for beef, a difference that probably accounts for the higher cell sodium in the latter. Exchange diffusion was faster in beef cells than in swine resulting in a larger tracer movement in beef. The exchange mechanism was temperature-sensitive, but was not inhibited by strophanthin. The unidirectional fluxes in canine cells were inhibited by low temperature, but they were sensibly unaffected by strophanthin. When placed in magnesium Ringer's solution (inhibits exchange diffusion in beef and swine cells) dog RBCs lost more than half of their internal sodium at a rate approximating the isotope flux in plasma or normal Ringer's solution. It was, however, not possible to separate the total tracer movement into pump, leak, and exchange.     

The glucose transport in retinal pigment epithelium is via passive facilitated diffusion

The glucose transport across the bovine retinal pigment epithelium (RPE) was studied in a modified Ussing chamber. Unidirectional fluxes were recorded with radioactive tracers L-[14C]-glucose (LG) and 3-O-methyl-D-[3H]-glucose (MDG). There was no significant difference between the unidirectional MDG fluxes (retina to choroid, and choroid to retina directions) with or without ouabain. The effects of two glucose transporter inhibitors, phloretin and cytochalasin B, on the glucose fluxes from choroid to retina cells were also investigated. The MDG flux was found to be inhibited by 45.5% by phloretin (10(-4) M) and 87.4% by cytochalasin B (10(-4) M). These inhibitory characteristics resembled the facilitated diffusion mode of glucose transport. The glucose transporter protein in the plasma membrane of RPE was located by means of photolabeling [3H]-cytochalasin B. The labeled plasma membrane enriched fraction was analysed by SDS-PAGE. The glucose transporter of bovine RPE was found to have a molecular weight range of 46-53 kDa. The molecular weight range of this transporter protein agreed with those of facilitated glucose transporters in other tissues indicating a molecular similarity between them. The results indicated that the glucose transport across the RPE is via passive facilitated diffusion.     

Model of ionic transport for bovine ciliary epithelium: effects of acetazolamide and HCO

The possible existence of transepithelial bicarbonate transport across the isolated bovine ciliary body was investigated by employing a chamber that allows for the measurement of unidirectional, radiolabeled fluxes of CO2 + HCO. No net flux of HCO was detected. However, acetazolamide (0.1 mM) reduced the simultaneously measured short-circuit current (I(sc)). In other experiments in which (36)Cl- was used, a net Cl- flux of 1.12 microeq. h(-1). cm(-2) (30 microA/cm(2)) in the blood-to-aqueous direction was detected. Acetazolamide, as well as removal of HCO from the aqueous bathing solution, inhibited the net Cl- flux and I(sc). Because such removal should increase HCO diffusion toward the aqueous compartment and increase the I(sc), this paradoxical effect could result from cell acidification and partial closure of Cl- channels. The acetazolamide effect on Cl- fluxes can be explained by a reduction of cellular H+ and HCO (generated from metabolic CO2 production), which exchange with Na+ and Cl- via Na+/H+ and Cl-/HCO exchangers, contributing to the net Cl- transport. The fact that the net Cl- flux is about three times larger than the I(sc) is explained with a vectorial model in which there is a secretion of Na+ and K+ into the aqueous humor that partially subtracts from the net Cl- flux. These transport characteristics of the bovine ciliary epithelium suggest how acetazolamide reduces intraocular pressure in the absence of HCO transport as a driving force for fluid secretion.     

The effect of ethanol on ion transport in frog skin.

Frog skin has been used as a model epithelial sodium-transporting system to study the effect of ethanol on ion transport. Treatment of the outside of frog skin with ethanol decreased the net sodium transport due to inhibition of 22Na+ influx. Ethanol did not alter sodium outflux when bathin the outside of the skin. The inhibition was in proportion to the concentration of ethanol, 0.25 M resulting in 50% inhibition. The chloride permeability of the skin was increased several-fold when the skin was exposed to ethanol in either bathing solution. With 0.4 M ethanol in the inner bathing solution, all the unidirectional fluxes of Na+ and C1- were increased. The movement of C1- was evaluated by comparison of C1- flux with urea flux, since urea is thought to move passively across frog skin via an extracellular (shunt) pathway. Chloride flux was increased to a greater extent than urea flux. These experiments indicate that ethanol affects chloride permeability beyond an increase in extracellular ion flow and independent of its effect of Na+ transport.     

Transport of butyrate across the isolated bovine rumen epithelium — interaction with sodium, chloride and bicarbonate

The Ussing chamber technique was used for studying unidirectional fluxes of ¹⁴C-butyrate across the bovine rumen epithelium in vitro. Significant amounts of butyrate were absorbed across the bovine rumen epithelium in vitro, without any external driving force. The paracellular pathway was quantitatively insignificant. The transcellular pathway was predominately voltage-insensitive. The serosal to mucosal (SM) pathway was regulated by mass action, whereas the mucosal to serosal (MS) pathway further includes a saturable process, which accounted for 30 to 55% of the MS flux. The studied transport process for ¹⁴C-butyrate across the epithelium could include metabolic processes and transport of ¹⁴C-labelled butyrate metabolites. The transport of butyrate interacted with Na⁺, Cl⁻ and HCO₃⁻, and there was a linear relationship between butyrate and sodium net transport. Lowering the sodium concentration from 140 to 10 mmol l⁻¹ decreased the butyrate MS flux significantly. Amiloride (1 mmol l⁻¹) did, however, not reduce the butyrate flux significantly. Chloride concentration in itself did not seem to influence the transport of butyrate, but chloride-free conditions tended to increase the MS and SM flux of butyrate by a DIDS-sensitive pathway. DIDS (bilateral 0.5 mmol l⁻¹) did further decrease the butyrate SM flux significantly at all chloride concentrations. Removing bicarbonate from the experimental solutions decreased the MS and increased the SM flux of butyrate significantly, and abolished net butyrate flux. There were no significant effects of the carbonic anhydrase inhibitor Acetazolamide (bilateral 1.0 mmol l⁻¹). The results can be explained by a model where butyrate and butyrate metabolites are transported both by passive diffusion and by an electroneutral anion-exchange with bicarbonate. The model couples sodium and butyrate via CO₂ from metabolism of butyrate, and intracellular pH.     

p-Aminohippurate transport in canine tracheal epithelium

The unidirectional fluxes of 20, 100, 500, and 2,000 microM rho-aminohippurate (PAH) were measured under open- and short-circuit conditions in canine tracheal epithelium mounted as flat sheets in Ussing chambers. In tissues pretreated with mucosal indomethacin (10(-6) M) and amiloride (10(-4) M), unidirectional PAH fluxes under short-circuit conditions increased with increasing bath concentrations but there was no significant net PAH transport. After stimulation of chloride secretion by mucosal cyclic adenosine 3',5' -cyclic monophosphate (cAMP 10(-3) M), there was a significant increase in the secretory flux of PAH and a significant decrease in the absorptive flux of PAH. This resulted in net PAH secretion that demonstrated saturation kinetics with an apparent Michaelis-Menten constant of 754 microM by Lineweaver-Burk analysis. Intracellular concentrations of PAH were 0.4-1.2 times bath concentrations after pretreatment with indomethacin and amiloride and increased to 2.6-3.3 times bath concentrations after cAMP. Under open-circuit conditions, secretory PAH flux decreased and absorptive flux increased resulting in net PAH absorption. We conclude from these early studies that the canine tracheal epithelium possesses a specialized system for the transport of organic anions in the airways and that this transport system may share many similarities with organic anion transport in the kidney.