Analysis of proximal tubule salt and water transport in standing droplets.

A mathematical model has been developed describing solute and water movement in the renal proximal tubule standing droplet experiment. The model explicitly incorporates the constraint of isosmotic reabsorption. Solute asymmetry due to the unequal distribution of protein, bicarbonate and other solutes between plasma and the standing droplet is shown to be one of the major reabsorptive forces; however, the introduction of an additional reabsorptive mechanism into the system equations is required in order to obtain a quantitative fit with experimental observations. The model demonstrates that limiting concentration gradients can be obtained in the absence of active transport and that their magnitudes will vary inversely with the permeability of the poorly permeant solute. Conversely, situations can occur where active transport will not elicit a limiting gradient. Consequently, previous interpretations of the meaning of limiting gradients and their magnitudes need to be reconsidered. The model further predicts that the technique for measuring non-electrolyte permeability using standing droplet experiments is likely to underestimate the true permeability. Finally, it is shown that a previous theoretical model of standing droplets, which does not explicitly include the constraint of isomotic reabsorption, cannot fit experimental data from proximal tubules.     

Passive Asymmetric Transport through Biological Membranes

The magnitude of passive diffusional solute transfer through artificial membranes is usually considered to be independent of the direction of the concentration gradient driving force. It can be shown, however, that a composite membrane, having as one component a membrane with a chemical reaction-facilitated diffusion transport mechanism, can result in an asymmetrical flux. An asymmetric flux caused by this type of structural heterogeneity may be one mechanism contributing to the asymmetric properties of biological membranes. Similar vectorial fluxes can be generated in interfacial solute transfer through membranes if hydrodynamic boundary layers occur at the membrane interface and reversible chemical reactions with the permeant species are involved in either phase.     

Anion regulation of active transport of protons across the membrane of the synaptic vesicles of the brain

The dependence of active transport of H+ on the presence of anions in synaptic vesicle membranes from rat brain was studied. The H+ transport was measured by monitoring the acidification of the vesicles with a permeant weak base-acridine orange. The fluorescence changes in the latter were proportional to the magnitude of artificially imposed pH gradients (delta pH). The ATP-dependent generation of delta pH was completely dependent on the presence of a permeant anion, was maximal at 150 mM Cl- and was inhibited, when the medium osmolarity was further increased by sucrose or KCl. At 150 mM only Br-, similar to Cl-, behaved as permeant anions, whereas I- was effective only at low (5-20 mM) concentrations. The anions--SCN-, ClO4-, HSO3- and I-(10-20 mM) as well as 4-acetamido-4'-isothiocyanatostilbene-2.2'-disulfonate (K0.5 = 14 microM) blocked the ATP-dependent generation of delta pH observed in the presence of Cl-, while other anions tested (F-, phosphate, bicarbonate, some organic anions) were virtually without effect and did not support the H+ transport. The dependence of the rate and extent of H+ accumulation on Cl- concentration was sigmoidal with a Hill coefficient of 2.8 and a Km value of 85-90 mM. The effects of anions point to the presence in the membrane of synaptic vesicles of an anion (chloride) channel whose conductance can regulate the H+ transport by switching it from an electrogenic to an electroneutral (coupled entry of H+ and Cl-) mode of operation.     

Acidification and ion permeabilities of highly purified rat liver endosomes

While it is well established that acidic pH in endosomes plays a critical role in mediating the orderly traffic of receptors and ligands during endocytosis, little is known about the bioenergetics or regulation of endosome acidification. Using highly enriched fractions of rat liver endosomes prepared by free flow electrophoresis and sucrose density gradient centrifugation, we have analyzed the mechanism of ATP-dependent acidification and ion permeability properties of the endosomal membrane. This procedure permitted the isolation of endosome fractions which were up to 200-fold enriched as indicated by the increased specific activity of ATP-dependent proton transport. Acidification was monitored using hepatocyte and total liver endosomes selectively labeled with pH-sensitive markers of receptor-mediated endocytosis (fluorescein isothiocyanate asialoorosomucoid) or fluid-phase endocytosis (fluorescein isothiocyanate-dextran). In addition, changes in membrane potential accompanying ATP-dependent acidification were directly measured using the voltage-sensitive fluorescent dye Di-S-C3(5). Our results indicate that ATP-dependent acidification of liver endosomes is electrogenic, with proton transport being accompanied by the generation of an interior-positive membrane potential opposing further acidification. The membrane potential can be dissipated by the influx of permeant external anions or efflux of internal alkali cations. Replacement externally of permeable anions with less permeable anions (e.g. replacing Cl- with gluconate) diminished acidification, as did replacement internally of a more permeant cation K+ with less permeant species (such as Na+ or tetramethylammonium). ATP-dependent H+ transport was not coupled to any specific anion or cation, however. The endosomal membrane was found to be extremely permeable to protons, with protons able to leak out almost as fast as they are pumped in. Thus, the internal pH of endosomes is likely to reflect a dynamic equilibrium of protons regulated by the intrinsic ion permeabilities of the endosomal membrane, in addition to the activity of an ATP-driven proton pump.     

Photophosphorylation as a function of illumination time. II. Effects of permeant buffers.

(1) The amounts of orthophosphate, bicarbonate and tris (hydroxymethyl)-aminomethane found inside the thylakoid are almost exactly the amounts predicted by assuming that the buffers equilibrate across the membrane. Since imidazole and pyridine delay the development of post-illumination ATP formation while increasing the maximum amount of ATP formed, it follows that such relatively permeant buffers must also enter the inner aqueous space of the thylakoid. (2) Photophosphorylation begins abruptly at full steady-state efficiency and full steady-state rate as soon as the illumination time exceeds about 5 ms when permeant ions are absent or as soon as the time exceeds about 50 ms if valinomycin and KC1 are present. In either case, permeant buffers have little or no effect on the time of illumination required to initiate phosphorylation. A concentration of bicarbonate which would delay acidification of the bulk of the inner aqueous phase for at least 350 ms has no effect at all on the time of initiation of phosphorylation. In somewhat swollen chloroplasts, the combined buffering by the tris(hydroxymethyl) aminomethane and orthophosphate inside would delay acidification of the inside by 1500 ms but, even in the presence of valinomycin and KC1, the total delay in the initiation of phosphorylation is then only 65 ms. Similar discrepancies occur with all of the other buffers mentioned. (3) Since these discrepancies between internal acidification and phosphorylation are found in the presence of saturating amounts of valinomycin and KC1, it seems that photophosphorylation can occur when there are no proton concentration gradients and no electrical potential differences across the membranes which separate the medium from the greater part of the internal aqueous phase. (4) We suggest that the protons produced by electron transport may be used directly for phosphorylation without even entering the bulk of the inner aqueous phase of the lamellar system. If so, phosphorylation could proceed long before the internal pH reflected the proton activity gradients within the membrane.     

Photophosphorylation as a function of illumination time. II. Effects of permeant buffers

(1) The amounts of orthophosphate, bicarbonate and tris(hydroxymethyl)-aminomethane found inside the thylakoid are almost exactly the amounts predicted by assuming that the buffers equilibrate across the membrane. Since imidazole and pyridine delay the development of post-illumination ATP formation while increasing the maximum amount of ATP formed, it follows that such relatively permeant buffers must also enter the inner aqueous space of the thylakoid.(2) Photophosphorylation begins abruptly at full steady-state efficiency and full steady-state rate as soon as the illumination time exceeds about 5 ms when permeant ions are absent or as soon as the time exceeds about 50 ms if valinomycin and KCl are present. In either case, permeant buffers have little or no effect on the time of illumination required to initiate phosphorylation. A concentration of bicarbonate which would delay acidification of the bulk of the inner aqueous phase for at least 350 ms has no effect at all on the time of initiation of phosphorylation. In somewhat swollen chloroplasts, the combined buffering by the tris(hydroxymethyl)aminomethane and orthophosphate inside would delay acidification of the inside by 1500 ms but, even in the presence of valinomycin and KCl, the total delay in the initiation of phosphorylation is then only 65 ms. Similar discrpancies occur with all of the other buffers mentioned.(3) Since these discrepancies between internal acidification and phosphorylation are found in the presence of saturating amounts of valinomycin and KCl, it seems that photophosphorylation can occur when there are no proton concentration gradients and no electrical potential differences across the membranes which separate the medium from the greater part of the internal aqueous phase.(4) We suggest that the protons produced by electron transport may be used directly for phosophorylation without ever entering the bulk of the inner aqueous phase of the lamellar system. If so, phosphorylation could proceed long before the internal pH reflected the proton activity gradients within the membrane.     

Dynamic loading of deformable porous media can induce active solute transport

Active solute transport mediated by molecular motors across porous membranes is a well-recognized mechanism for transport across the cell membrane. In contrast, active transport mediated by mechanical loading of porous media is a non-intuitive mechanism that has only been predicted recently from theory, but not yet observed experimentally. This study uses agarose hydrogel and dextran molecules as a model experimental system to explore this mechanism. Results show that dynamic loading can enhance the uptake of dextran by a factor greater than 15 over passive diffusion, for certain combinations of gel concentration and dextran molecular weight. Upon cessation of loading, the concentration reverts back to that achieved under passive diffusion. Thus, active solute transport in porous media can indeed be mediated by cyclical mechanical loading.     

Studies of the Ca2+ transport mechanism of human erythrocyte inside-out membrane vesicles. Evidence for the development of a positive interior membrane potential

Previous observations on the effects of permeant anions on ATP-dependent calcium transport in inside-out vesicles prepared from human erythrocytes suggested that the calcium pump is electrogenic, generating a positive interior membrane potential. The present work demonstrates the development of a positive interior membrane potential across inside-out vesicle membranes during calcium transport in the absence of permeant anions. Several membrane potential probes, 1-anilino-8-naphthalenesulfonate, 3,3'-dipropylthiodicarbocyanine iodide, and an electron paramagnetic resonant triphenylphosphonium derivative, provide qualitative evidence for the development of a membrane potential. Moreover, a number of parallels are observed between the changes in the membrane potential measured by the probes and calcium transport. These include enhancement by calmodulin, time course of change, similar kinetic properties, and the requirement for intact vesicle membranes. Quantitative measurements of the membrane potential shows a positive interior membrane potential of 26-37 mV using radiolabeled permeant anion distribution and 38-57 mV using 3,3'-dipropylthiodicarbocyanine iodide fluorescence changes. These membrane potentials are of a similar magnitude to those reported for the sarcoplasmic reticulum calcium pump (Zimniak, P., and Racker, E. (1978). J. Biol. Chem. 253, 4631-4637).     

Nuclear magnetic resonance studies of cation transport across vesicle bilayer membranes.

We analyze an increasingly popular NMR method analogous to the black lipid membrane (BLM) isotopic tracer experiment for the study of mediated cation transport but involving the preparation of vesicles with an environment asymmetric in that paramagnetic metal ions are present only outside the vesicles. This asymmetry is manifest in the NMR spectrum as two distinct resonances for magnetic nuclei in outside and inside lipid headgroups. As mediated transport begins and for the paramagnetic metal ions enter the vesicles, the inner headgroup resonance line shifts and changes shape with a time course containing much information on the actual ion transport mechanism. Processes by which the ions enter the vesicles one or a few at a time (such as via a diffusive carrier) are easily distinguishable from those by which the ions enter in large bursts (such as by pore activation). The limiting case where intervesicular mediator exchange is slow relative to cation transport (the situation for integral membrane proteins) is treated analytically. Computer simulated curves indicate conditions necessary for certain changes in the line shape which are analogous to the "current jumps" observed in BLM conductance studies. The theory derived allows estimates of the average number of ions entering the first few bursts, how often the bursts occur, and how they depend on the concentration of the mediating species in the vesicular membrane. Preliminary experimental spectra illustrating some of the various possible line shape behaviors are presented.     

Protein fluxes along the filopodium as a framework for understanding the growth-retraction dynamics

We present a picture of filopodial growth and retraction from physics perspective, where we emphasize the significance of the role played by protein fluxes due to spatially extended nature of the filopodium. We review a series of works, which used stochastic simulations and mean field analytical modeling to find the concentration profile of G-actin inside a filopodium, which, in turn, determines the stationary filopodial length. In addition to extensively reviewing the prior works, we also report some new results on the role of active transport in regulating the length of filopodia. We model a filopodium where delivery of actin monomers towards the tip can occur both through passive diffusion and active transport by myosin motors. We found that the concentration profile of G-actin along the filopodium is rather non-trivial, containing a narrow minimum near the base followed by a broad maximum. For efficient enough actin transport, this non-monotonous shape is expected to occur under a broad set of conditions. We also raise the issue of slow approach to the stationary length and the possibility of multiple steady state solutions.     

Protein fluxes along the filopodium as a framework for understanding the growth-retraction dynamics: The interplay between diffusion and active transport

We present a picture of filopodial growth and retraction from physics perspective, where we emphasize the significance of the role played by protein fluxes due to spatially extended nature of the filopodium. We review a series of works, which used stochastic simulations and mean field analytical modeling to find the concentration profile of G-actin inside a filopodium, which, in turn, determines the stationary filopodial length. In addition to extensively reviewing the prior works, we also report some new results on the role of active transport in regulating the length of filopodia. We model a filopodium where delivery of actin monomers toward the tip can occur both through passive diffusion and active transport by myosin motors. We found that the concentration profile of G-actin along the filopodium is rather non-trivial, containing a narrow minimum near the base followed by a broad maximum. For efficient enough actin transport, this non-monotonous shape is expected to occur under a broad set of conditions. We also raise the issue of slow approach to the stationary length and the possibility of multiple steady-state solutions.Key words: filopodia, active transport, molecular motors, stochastic process, mean-field theory     

Light-induced proton permeability changes in retinal rod photoreceptor disk membranes.

We have used the membrane-permeant charged fluorescent dye, 3,3'-dipropylthiadicarbocyanine iodide (diS-C3[5]), to monitor electrical potentials across the membranes of isolated bovine disks. Calibration curves obtained from experiments where a potential was created across the disk membrane by a potassium concentration gradient and valinomycin showed an approximately linear relation between dye fluorescence and calculated membrane potential from 0 to -120 mV. Light exposure in the presence of the permeant buffer, imidazole, caused a rapid decay of the membrane potential to a new stable level. Addition of CCCP, a proton ionophore, in the dark produced the same effect as illumination. When the permeant buffer, imidazole, was replaced by the impermeant buffer, Hepes, neither light nor CCCP discharged the gradient. We interpret the changes in membrane potential measured upon illumination to be the result of a light-induced increase in the permeability of the disk membrane to protons. A permeant buffer is required to prevent the build-up of a pH gradient which would inhibit the sustained proton flow needed for an observable change in membrane potential.     

Vesicular and nonvesicular transport of ceramide from ER to the Golgi apparatus in yeast.

Transport and sorting of lipids must occur with specific mechanisms because the membranes of intracellular organelles differ in lipid composition even though most lipid biosynthesis begins in the ER. In yeast, ceramide is synthesized in the ER and transferred to the Golgi apparatus where inositolphosphorylceramide (IPC) is formed. These two facts imply that ceramide can be transported to the Golgi independent of vesicular traffic because IPC synthesis still continues when vesicular transport is blocked in sec mutants. Nonvesicular IPC synthesis in intact cells is not affected by ATP depletion. Using an in vitro assay that reconstitutes the nonvesicular pathway for transport of ceramide, we found that transport is temperature and cytosol dependent but energy independent. Preincubation of ER and Golgi fractions together at 4 degrees C, where ceramide transport does not occur, rendered the transport reaction membrane concentration independent, providing biochemical evidence that ER-Golgi membrane contacts stimulate ceramide transport. A cytosolic protease-sensitive factor is required after establishment of ER-Golgi contacts.     

Effects of pipette geometry on the time course of solution change in patch clamp experiments.

The time course of change in current through KATP channels in inside-out membrane patches, after step change of permeant ion (K+) concentration, was measured. A simple model of the patch as a membrane disc at the base of a cone with the apex removed, was able to describe the time course of channel activity after step change of [K+]. By measuring pipette geometry and using jumps of [permeant ion], it was then possible to estimate the time course of concentration at the membrane for jumps of any other ion or gating ligand. A simple channel block mechanism was used to simulate experiments with concentration jumps of a blocking ligand. The rate constants for ligand-channel interaction were extracted by least-squares fitting of computed mass action responses to those observed in simulated experiments. The simulations showed that even with diffusion delays of hundreds of milliseconds (as may occur in inside-out patch experiments), ligand association and dissociation rates of up to 1,000 s-1 could be accurately extracted by this approach. The approach should be generally applicable to the analysis of ligand concentration jump experiments on any ion channel whose activity is modulated by intracellular ligand.     

Potassium modulation of taurine transport across the frog retinal pigment epithelium

Net taurine transport across the frog retinal pigment epithelium-choroid was measured as a function of extracellular potassium concentration, [K+]o. The net rate of retina-to-choroid transport increased monotonically as [K+]o increased from 0.2 mM to 2 mM on the apical (neural retinal) side of the tissue. No further increase was observed when [k+]o was elevated to 5 mM. The [K+]o changes that modulate taurine transport approximate the light-induced [K+]o changes that occur in the extracellular space separating the photoreceptors and the apical membrane of the pigment epithelium. The taurine-potassium interaction was studied by using rubidium as a substitute for potassium and measuring active rubidium transport as a function of extracellular taurine concentration. An increase in apical taurine concentration, from 0.2 mM to 2 mM, produced a threefold increase in active rubidium transport, retina to choroid. Net taurine transport can also be altered by relatively large, 55 mM, changes in [Na+]o. Apical ouabain, 10(-4) M, inhibited active taurine, rubidium, and potassium transport; in the case of taurine, this inhibition is most likely due to a decrease in the sodium electrochemical gradient. In sum, these results suggest that the apical membrane contains a taurine, sodium co-transport mechanism whose rate is modulated, indirectly, through the sodium pump. This pump has previously been shown to be electrogenic and located on the apical membrane, and its rate is modulated, indirectly, by the taurine co-transport mechanism.     

Direct evidence for the role of the membrane potential in glutathione transport by renal brush-border membranes

Transport of GSH was studied in isolated rat kidney cortical brush-border membrane vesicles in which gamma-glutamyltransferase had been inactivated by a specific affinity labeling reagent, L-(alpha S,5S)-alpha-amino-3-chloro-4,5-dihydro-5-isoxazoleacetic acid (AT-125). Transport of intact 2-3H-glycine-labeled GSH occurred into an osmotically active intravesicular space of AT-125-treated membranes. The initial rate of transport followed saturation kinetics with respect to GSH concentrations; an apparent Km of 0.21 mM and Vmax of 0.23 nmol/mg protein X 20 were calculated at 25 degrees C with a 0.1 M NaCl gradient (vesicle inside less than vesicle outside). Sodium chloride in the transport medium could be replaced with KCl without affecting transport activity. The rate of GSH uptake was enhanced by replacing KCl in the transport medium with K2SO4, providing a less permeant anion, and was reduced by replacing KCl with KSCN, providing a more permeant anion. The rate of GSH transport markedly decreased in the absence of a K+ gradient across the vesicular membranes and was enhanced by a valinomycin-induced K+ diffusion potential (vesicle-inside-positive). These results indicate that GSH transport is dependent on membrane potential and involves the transfer of negative charge. The rate of GSH transport was inhibited by S-benzyl glutathione but not by glycine, glutamic acid, and gamma-glutamyl-p-nitroanilide. When incubated with [2-3H]glycine-labeled GSH, intact untreated vesicles also accumulated radioactivity; the rate of uptake was significantly higher in a Na+ gradient than in a K+ gradient. Sodium-dependent transport, but not sodium-independent uptake, was almost completely inhibited by a high concentration of unlabeled glycine. At equilibrium, most of the radioactivity which accumulated in the intravesicular space was accounted for by free glycine. These results suggest that GSH which is secreted into the tubular lumen by a specific translocase in the lumenal membranes or filtered by the glomerulus may be degraded in situ by membranous gamma-glutamyltransferase and peptidase activities which hydrolyze peptide bonds of cysteinylglycine and its derivatives. The resulting free amino acids can be reabsorbed into tubule cells by sodium-dependent transport systems in renal cortical brush-border membranes.     

General method for the derivation and numerical solution of epithelial transport models

Summary A general method is presented for the formulation and numerical evaluation of mathematical models describing epithelial transport. The method is based on the principles of conservation of mass, and maintenance of electroneutrality within the cells and bathing solutions. It is therefore independent of the specific membrane transport mechanisms, and can be used to evaluate different models describing arbitrary transport processes (including passive, active and cotransport processes). Detailed numerical methods are presented that allow computation of steady-state and transient responses under open-circuit, current-clamp and voltage-clamp conditions, using a general-purpose laboratory minicomputer. To evaluate the utility of this approach, a specific model is presented that is consistent with the Koefoed-Johnson and Ussing hypothesis of sodium transport in tight epithelia (Acta Physiol. Scand. 42:298–308, 1958). This model considers passive transport of an arbitrary number of permeant solutes, active transport of sodium and potassium, and osmotically induced water transport across the apical and basolateral membranes. Results of the model are compared to published experimental measurements in rabbit urinary bladder epithelium.     

Optimization criteria of the mechanism governing the stability of the membrane potential

For small changes in ion concentration within the physiological range the membrane potential transients can be explained in terms of two linear models both for passive and active transport. Using frog sartorius muscle as a suitable model system the ion pump is considered to work within the steepest range of the flux-concentration characteristic. Further for the small perturbations the equations describing passive ion transport can be safely linearized. The conclusion appears inescapable that for the muscle membrane the intracellular ion concentration adjusts itself in some optimal manner to the level of the extracellular ions. The active ion transport represents a control parameter for the membrane potential. The model structure corresponds to a dynamic system, the control processes of which are optimized with respect to a quadratic integral-criterion function. Here, both the performance index of the control sequence in the membrane processes and the energy consumed by the ion fluxes have been considered for small perturbations of Na⁺, K⁺, and Cl^? in the neighbourhood of the physiological working point. As it is, the control system governing the active and passive ion transport processes is essentially optimized with respect to a minimal energy usage. The amount of energy consumed during the transients predicted by the model has been calculated.     

A model for axonal propagation incorporating both radial and axial ionic transport.

We present an axonal model that explicitly includes ionic diffusion in the intracellular, periaxonal, and extracellular spaces and that incorporates a Hodgkin-Huxley membrane, extended with potassium channel inactivation and active ion transport. Although ionic concentration changes may not be significant in the time course of one action potential, they are important when considering the long-term behavior (seconds to minutes) of an axon. We demonstrate this point with simulations of transected axons where ions are moving between the intra- and extracellular spaces through an opening that is sealing with time. The model predicts that sealing must occur within a critical time interval after the initial injury to prevent the entire axon from becoming permanently depolarized. This critical time interval becomes considerably shorter when active ion transport is disabled. Furthermore, the model can be used to study the effects of sodium and potassium channel inactivation; e.g., sodium inactivation must be almost complete (within 0.02%) to obtain simulation results that are realistic.     

Structured bienzymatical models formed by sequential enzymes bound into artificial supports: Active glucose transport effect

Summary Two different artificial membrane systems bearing two built-in sequential enzymes are studied and compared in this communication.The first is a nonstructured membrane bearing two mixed enzymes: -galactosidase and glucose-oxidase. Its use enables a mathematical model to be formulated describing the heterogeneous phase kinetics of a bienzymatic system. The second is a multi-layer membrane system in which the structural dissymmetry involves a spatial orientation of the reacting metabolites, resulting in active glucose transport.The latter system consists of two active leaflets, the first phosphorylating glucose (hexokinase+ATP), the second dephosphorylating glucose-6 phosphate (phosphatase). On either side of this system, a perm-selective proteic layer allows the passage of glucose but not of glucose-6 phosphate. When positioned between two compartments containing glucose, such a membrane accumulates glucose on its phosphatase side, while degrading ATP.The accumulation of glucose as a function of the initial concentration shows the classical saturation of the transport system. Fructose competes with glucose transport.The chemical balance of these two reactions has the appearance of hydrolysis of ATP. Vectorial catalysis is a result of the dissymmetry in distribution of active sites and can be explained by an oscillatory concentration profile of glucose inside the membrane.The bienzymatic mechanism, a model of which is given here, is valid for any thickness of active layers and applicable to a system where both active sides are part of the same molecule as soon as it forms a uniformly oriented monolayer throughout the membrane structure.