The independence principle. A reconsideration

The electrodiffusion model presented in the previous paper, which specifically excludes ion-ion interactions, is analyzed for the ratio of one-way fluxes (flux ratio) as a function of the ionic driving force across the membrane. Significant deviations from the behavior expected on the basis of the Ussing relation are found. These are sufficient to explain the “nonindependent” ion movement noted in some biological flux ratio data. One-way fluxes are dependent on the ionic concentration on both sides of the membrane. The coupling of these fluxes to ionic concentrations comes from the dependence of ionic mobility and the diffusion coefficient on the equilibrium potential. It is concluded that nonindependent behavior in experimental data is not sufficient to implicate ion-ion interaction as the source of the discrepancy.     

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").     

Mass Transfer in the Cornea: I. Interacting Ion Flows in an Arbitrarily Charged Membrane

The formalisms of irreversible thermodynamics are used to describe multi-ionic nonconvective flow through an arbitrarily charged membrane. Interactions between oppositely charged ions are included and are measured by a single phenomenological coefficient. The consequent generalized Nernst-Planck flux equations are integrated to yield a relation between the species fluxes and the composition of the solutions bounding the membrane. It is assumed in the derivation that activity coefficient gradients within the membrane and direct interactions between ions of like charge are negligible. Some special cases are examined. To illustrate the use of the final equations, a single membrane separating solutions of differing composition is modeled, and the effect of ion-ion interactions on the membrane potential and the ion fluxes is demonstrated for several values of diffusion current density and membrane charge density.     

The Potassium Flux Ratio in Skeletal Muscle As a Test for Independent Ion Movement

The flux ratio of potassium ions was measured on frog sartorius muscle under conditions in which a substantial net potassium loss occurs. Muscle fiber membrane potentials were measured under identical conditions. The observed flux ratios were compared with values calculated from a theoretical relation derived on the assumptions that the unidirectional fluxes are both passive and occur independently. The results favor the conclusion that the potassium fluxes across skeletal muscle membrane occur along passive electrochemical gradients and obey the independence principle.     

Unidirectional K+ fluxes through recombinant Shaker potassium channels expressed in single Xenopus oocytes

We describe a method to evaluate the ratio of ionic fluxes through recombinant channels expressed in a single Xenopus oocyte. A potassium channel encoded by the Drosophila Shaker gene tested by this method exhibited flux ratios far from those expected for independent ion movement. At a fixed extracellular concentration of 25 mM K+, this channel showed single-file diffusion with an Ussing flux-ratio exponent, n', of 3.4 at a membrane potential of -30 mV. There was an apparent, small voltage dependence of this parameter with n' values of 2.4 at -15 and -5 mV. These results indicate that the pore in these channels can simultaneously accommodate at least four K+ ions. If each of these K+ ions is in contact with two water molecules, the minimum length of the pore is 24 A.     

Conformational model for ion permeation in membrane channels: a comparison with multi-ion models and applications to calcium channel permeability.

The permeation properties of ion channels existing in several conductive states were analyzed. Each state was represented by the one-ion model. A special emphasis was placed on features, assumed to be indicative of a multi-ion mode of channel occupancy such as a deviation of concentration dependence of channel conductance from the Michaelis-Menten equation, an anomalous mole fraction effect, a strong voltage dependence of ion block and coupling of unidirectional fluxes (anomalous Ussing flux ratio). The conformational model was shown to have all these properties. The ion permeation through voltage-sensitive calcium channels fulfilled all the characteristics of the model proposed.     

Active Ion Transport Across Canine Blood Vessel Walls

Experiments giving evidence of active Na and Cl ion fluxes across large canine blood vessel walls (aorta, vena cava) in vitro have been presented. The information has been obtained using ion tracer techniques after Ussing and with diffusion cells of the Hogben type. The available data suggest that the membranes are satisfactorily oxygenated by the bathing solutions saturated with oxygen at atmospheric pressure. Evidence is offered which indicates that active ion transport does occur across the aorta and vena cava in in vitro experiments. Under the conditions of the experiment net Na and Cl flux takes place from intima to adventitia across the aorta, and from adventitia to intima across the vena cava at low measured potential differences. The possible relationships of derangement of active ion transport mechanisms, produced by electric currents and tissue injury potential differences, to intravascular thrombosis are alluded to. It would appear that sodium and chloride fluxes across large blood vessel walls in vitro occur at least in part as the result of metabolic processes and cannot be explained simply on the basis of diffusion across a semipermeable membrane.     

Dynamic property of membrane formation in a protoplasmic droplet of Nitella

A theory is presented to explain the dynamic characteristics of an electric potential and the resistance of a surface membrane during the formation of a protoplasmic droplet isolated from Nitella. Basic equations are coupled ones for describing ion concentrations near the surface of the droplet, active and passive ion fluxes on the surface, and kinetics of membrane-constituting molecules diffusing from the inside of the protoplasm. The present results give a good explanation of the observed kinetics of electric properties throughout the formative process of surface membranes after the ion concentrations are replaced by lower ones. The results can also explain well the observed data on the steady state. Oscillatory changes in the membrane potential induced by ions strongly adsorbed on the surface membrane are discussed in relation to growth and regeneration phenomena in biological systems such as bean roots and Acetabularia.     

Correlation of Electrical and Permeability Properties of Ion-Selective Membranes

The linear phenomenological equations giving particle and practical fluxes of a single electrolyte across an ion-selective membrane are stated and interrelated. It is shown that the experimental measurements commonly made in biological and synthetic membrane studies may be used, with minor modification, to obtain the phenomenological transport coefficients and their concentration dependences. It is demonstrated that the electrical properties of a homogeneous membrane may be obtained as functions of the bathing solution concentration by combining fluxes measured under open and short circuit. Attention is paid to the use of radiotracers when measuring ionic fluxes. To obtain all the phenomenological coefficients at least one measurement must be made under a pressure gradient. The experimental difficulties in such measurements are discussed and the merits and demerits of various experiments considered. The problems of measuring potentials and concentrations at the low pressure face of a supported membrane make several mathematically simple approaches experimentally unattractive. The best methods appear to be either the measurement of a succession of “apparent osmotic pressures” under concentration differences sufficiently small that the membrane does not require support or the study of “reverse osmosis”. Sets of equations are given which enable the phenomenological coefficients to be evaluated from convenient experiments. With a stable homogeneous membrane nine coefficients may be obtained thus enabling either the applicability of the reciprocal relations or the applicability of linear theory under the conditions of the experiments to be tested. For a discontinuous system the six independent coefficients may be obtained from experiments in a single membrane cell.     

Steady-state voltages, ion fluxes, and volume regulation in syncytial tissues.

Equations are developed that describe the steady-state relationships among ion fluxes, solute fluxes, water flow, voltage, concentration of solute, and hydrostatic pressure in a spherically symmetrical syncytial tissue. Each cell of the syncytium is assumed to have membrane channels for Na, K, and Cl, a membrane pump for Na/K, and some concentration of intracellular protein of net negative charge. However, the surface cells and inner cells of the tissue are assumed to have different distributions of membrane transport properties, hence there is a radial circulation of fluxes and a radial distribution of forces. Some reasonable approximations are made that allow analytic solutions of the nonlinear differential equations. These solutions are used to analyze data from the frog lens and are shown to account for the known steady-state properties of this tissue. Moreover, these solutions are used to make predictions on other steady-state properties, which have not been directly measured, and graphical results on the circulation of water, ions and solute through the frog lens are presented.     

Basolateral Mg2+/Na+ exchange regulates apical nonselective cation channel in sheep rumen epithelium via cytosolic Mg2+

High potassium diets lead to an inverse regulation of sodium and magnesium absorption in ruminants, suggesting some form of cross talk. Previous Ussing chamber experiments have demonstrated a divalent sensitive Na(+) conductance in the apical membrane of ruminal epithelium. Using patch-clamped ruminal epithelial cells, we could observe a divalent sensitive, nonselective cation conductance (NSCC) with K(+) permeability > Cs(+) permeability > Na(+) permeability. Conductance increased and rectification decreased when either Mg(2+) or both Ca(2+) and Mg(2+) were removed from the internal or external solution or both. The conductance could be blocked by Ba(2+), but not by tetraethylammonium (TEA). Subsequently, we studied this conductance measured as short-circuit current (I(sc)) in Ussing chambers. Forskolin, IBMX, and theophylline are known to block both I(sc) and Na transport across ruminal epithelium in the presence of divalent cations. When the NSCC was stimulated by removing mucosal calcium, an initial decrease in I(sc) was followed by a subsequent increase. The cAMP-mediated increase in I(sc) was reduced by low serosal Na(+) and serosal addition of imipramine or serosal amiloride and depended on the availability of mucosal magnesium. Luminal amiloride had no effect. Flux studies showed that low serosal Na(+) reduced (28)Mg fluxes from mucosal to serosal. The data suggest that cAMP stimulates basolateral Na(+)/Mg(2+) exchange, reducing cytosolic Mg. This increases sodium uptake through a magnesium-sensitive NSCC in the apical membrane. Likewise, the reduction in magnesium uptake that follows ingestion of high potassium fodder may facilitate sodium absorption, as observed in studies of ruminal osmoregulation. Possibly, grass tetany (hypomagnesemia) is a side effect of this useful mechanism.     

Bidirectional reaction steps in metabolic networks: II. Flux estimation and statistical analysis

Metabolic carbon labelling experiments enable a large amount of extracellular fluxes and intracellular carbon isotope enrichments to be measured. Since the relation between the measured quantities and the unknown intracellular metabolic fluxes is given by bilinear balance equations, flux determination from this data set requires the numerical solution of a nonlinear inverse problem. To this end, a general algorithm for flux estimation from metabolic carbon labelling experiments based on the least squares approach is developed in this contribution and complemented by appropriate tools for statistical analysis. The linearization technique usually applied for the computation of nonlinear confidence regions is shown to be inappropriate in the case of large exchange fluxes. For this reason a sophisticated compactification transformation technique for nonlinear statistical analysis is developed. Statistical analysis is then performed by computing appropriate statistical quality measures like output sensitivities, parameter sensitivities and the parameter covariance matrix. This allows one to determine the order of magnitude of exchange fluxes in most practical situations. An application study with a large data set from lysine-producing Corynebacterium glutamicum demonstrates the power and limitations of the carbon-labelling technique. It is shown that all intracellular fluxes in central metabolism can be quantitated without assumptions on intracellular energy yields. At the same time several exchange fluxes are determined which is invaluable information for metabolic engineering. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55: 118-135, 1997.     

Potassium transport by rabbit descending colon, in vitro

Studies of the bidirectional fluxes of K across segments of rabbit descending colon indicate that: a) when the tissue is short-circuited, the net flux does not differ significantly from zero under control conditions and in the presence of aldosterone; and b) the bidirectional fluxes of K conform to the Ussing flux-ratio equation over a wide range of transepithelial electrochemical potential differences. These and other findings strongly suggest that the movements of K across the epithelium are restricted to paracellular routes and are entirely passive. Studies dealing with the mechanism of homocellular K transport indicate that: a) K is actively transported into the cells across the basolateral membranes against an electrochemical potential difference of approximately 30 mV; and b) the active uptake of K may be mediated by a rheogenic Na-K exchange pump that is also responsible for transcellular Na transport. These results are entirely consistent with the model proposed by Koefoed-Johnson and Ussing for isolated frog skin.     

Asymmetric [14C]albumin transport across bullfrog alveolar epithelium

Bullfrog lungs were prepared as planar sheets and bathed with Ringer solution in Ussing chambers. In the presence of a constant electrical gradient (20, 0, or -20 mV) across the tissue, 14C-labeled bovine serum albumin or inulin was instilled into the upstream reservoir and the rate of appearance of the tracer in the downstream reservoir was monitored. Two lungs from the same animal were used to determine any directional difference in tracer fluxes. An apparent permeability coefficient was estimated from a relationship between normalized downstream radioactivities and time. Results showed that the apparent permeability of albumin in the alveolar to pleural direction across the alveolar epithelial barrier is 2.3 X 10(-7) cm/s, significantly greater (P less than 0.0005) than that in the pleural to alveolar direction (5.3 X 10(-8) cm/s) when the tissue was short circuited. Permeability of inulin, on the other hand, did not show any directional dependence and averaged 3.1 X 10(-8) cm/s in both directions. There was no effect on radiotracer fluxes permeabilities of different electrical gradients across the tissue. Gel electrophoretograms and corresponding radiochromatograms suggest that the large and asymmetric isotope fluxes are not primarily due to digestion or degradation of labeled molecules. Inulin appears to traverse the alveolar epithelial barrier by simple diffusion through hydrated paracellular pathways. On the other hand, [14C]albumin crosses the alveolar epithelium more rapidly than would be expected by simple diffusion. These asymmetric and large tracer fluxes suggest that a specialized mechanism is present in alveolar epithelium that may be capable of helping to remove albumin from the alveolar space.     

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.     

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).     

Avian renal proximal tubule epithelium urate secretion is mediated by Mrp4

Birds are uricotelic and, like humans, maintain high plasma urate concentrations (approximately 300 microM). The majority of their urate waste, as in humans, is eliminated by renal proximal tubular secretion; however, the mechanism of urate transport across the brush-border membrane of the intact proximal tubule epithelium during secretion is uncertain. The dominance of secretory urate transport in the bird provides a convenient model for examining this process. The present study shows that short hairpin RNA interference (shRNAi) effectively knocked down gene expression of multidrug resistance protein 4 (Mrp4; 25% of control) in primary monolayer cultures of isolated chicken proximal tubule epithelial cells (cPTCs). Control and Mrp4-shRNAi-treated cPTCs were mounted in Ussing chambers and unidirectional transepithelial fluxes of urate were measured. To detect nonspecific effects, transepithelial electrical resistance (TER) and sodium-dependent glucose transport (Iglu) were monitored throughout experiments. Knocking down Mrp4 expression resulted in a reduction of transepithelial urate secretion to 35% of control with no effects on TER or Iglu. Although electrical gradient-driven urate transport in isolated brush-border membrane vesicles was confirmed, potassium-induced depolarization of the plasma membrane in intact cPTCs failed to inhibit active transepithelial urate secretion. However, electrical gradient-dependent vesicular urate transport was inhibited by the MRP4 inhibitor MK-571 also known to inhibit active transepithelial urate transport by cPTCs. Based on these data, direct measure of active transepithelial urate secretion in functional avian proximal tubule epithelium indicates that Mrp4 is the dominant apical membrane exit pathway from cell to lumen.     

The kinetics of colloid osmotic hemolysis. I. Nystatin-induced lysis

A kinetic model of colloid osmotic hemolysis for cation-permeable cells has been developed. The model consists of three essential components. The first is a set of flux equations, under the assumption that the membrane potential is equal to the chloride equilibrium potential and that cation fluxes are described by the Goldman flux equation. The second is the osmotic equilibrium model of Freedman and Hoffman that takes into account the non-ideal osmotic behavior of erythrocytes. The third is an empirical relation between hemolysis and cell volume, developed from the lysis behavior in hypoosmotic media. Model simulations are compared with lysis experiments using the antibiotic nystatin to raise cation permeability. The form of the kinetics and inhibition of lysis by sucrose are described well by the model. In additional lysis experiments at different external pH the small pH dependence is accounted for by the model.     

Turgor Pressure Regulation in Valonia utricularis: Effect of Cell Wall Elasticity and Auxin

The electrical membrane resistance rho(0) of the marine alga Valonia utricularis shows a marked maximum in dependence on the turgor pressure. The critical pressure, P(c), at which the maximum occurs, as well as its absolute value, rho(0) (max), are strongly volume-dependent. Both P(c) and rho(0) (max), increase with decreasing cell volume. It seems likely, that these relationships reflect the elastic properties of the cell wall, because the volumetric elastic modulus, epsilon, is also volume-dependent, increasing hyperbolically with cell volume. Both P(c) and rho(0) (max) can be affected by external application of indole-3-acetic acid at concentrations of 2.10(-7)m to 2 .10(-5)m. The critical pressure is shifted by 1.2 to 6 bars toward higher pressures and the maximum membrane resistance increased up to 5.6-fold. During the course of the experiments (up to 4 hours), however, IAA had no effect on the volumetric elastic modulus, epsilon.The maximum in membrane resistance is discussed in terms of a pressure-dependent change of potassium fluxes. The volume dependence of P(c) and rho(0) (max) suggests that not only turgor pressure but also epsilon must be considered as a regulating parameter during turgor pressure regulation. On this basis a hypothesis is presented for the transformation of both, a pressure signal and of changes in the elastic properties of the cell wall into alterations of ion fluxes. It is assumed that the combined effects of tension and compression of the membranes as well as the interaction between membrane and cell wall opposingly change the number of transport sites for K(+) providing a turgor-sensing mechanism that regulates ion fluxes. The IAA effects demonstrated are consistent with this view, suggesting that the basic mechanisms for turgor pressure regulation and growth regulation are similar.Any relation connecting growth rate with turgor pressure should be governed by two parameters, i.e. by a yielding pressure, at which cell growth starts, and by the critical pressure, at which it ceases again.