Sensitivity Analysis of Flux Determination in Heart by H218O -provided Labeling Using a Dynamic Isotopologue Model of Energy Transfer Pathways

To characterize intracellular energy transfer in the heart, two organ-level methods have frequently been employed: inversion and saturation transfer, and dynamic labeling. Creatine kinase (CK) fluxes obtained by following oxygen labeling have been considerably smaller than the fluxes determined by saturation transfer. It has been proposed that dynamic labeling determines net flux through CK shuttle, whereas saturation transfer measures total unidirectional flux. However, to our knowledge, no sensitivity analysis of flux determination by oxygen labeling has been performed, limiting our ability to compare flux distributions predicted by different methods. Here we analyze oxygen labeling in a physiological heart phosphotransfer network with active CK and adenylate kinase (AdK) shuttles and establish which fluxes determine the labeling state. A mathematical model consisting of a system of ordinary differential equations was composed describing enrichment in each phosphoryl group and inorganic phosphate. By varying flux distributions in the model and calculating the labeling, we analyzed labeling sensitivity to different fluxes in the heart. We observed that the labeling state is predominantly sensitive to total unidirectional CK and AdK fluxes and not to net fluxes. We conclude that measuring dynamic incorporation of into the high-energy phosphotransfer network in heart does not permit unambiguous determination of energetic fluxes with a higher magnitude than the ATP synthase rate when the bidirectionality of fluxes is taken into account. Our analysis suggests that the flux distributions obtained using dynamic labeling, after removing the net flux assumption, are comparable with those from inversion and saturation transfer.     

Studies on the Movement of Water through the Isolated Toad Bladder and Its Modification by Vasopressin

Measurements of diffusion permeability and of net transfer of water have been made across the isolated urinary bladder of the toad, Bufo marinus, and the effects thereon of mammalian neurohypophyseal hormone have been examined. In the absence of a transmembrane osmotic gradient, vasopressin increases the unidirectional flux of water from a mean of 340 to a mean of 570 µl per cm² per hour but the net water movement remains essentially zero. In the presence of an osmotic gradient but without hormone net transfer of water remains very small. On addition of hormone large net fluxes of water occur; the magnitude of which is linearly proportional to the osmotic gradient. The action of the hormone on movement of water is not dependent on the presence of sodium or on active transport of sodium. Comparison of the net transport of water and of unidirectional diffusion permeability of the membrane to water indicates that non-diffusional transport must predominate as the means by which net movement occurs in the presence of an osmotic gradient. An action of the hormone on the mucosal surface of the bladder wall is demonstrated. The effects of the hormone on water movement are most simply explained as an action to increase the permeability and porosity of the mucosal surface of the membrane.     

Unidirectional fluxes and blood flow

Unidirectional fluxes determined in vivo (in experiments with intact blood supply) on the basis of the permeation rate of labeled molecules are functions of the absorption site blood flow rate. As the permeability of the substances increases, the “blood flow-independent” unidirectional flux changes to a “blood flow-limited” flux. By contrast, the ratio of unidirectional fluxes is independent of blood flow, provided that permeation of the substance out of the draining capillaries is proportional to the concentration and the permeation into the opposite direction does not depend on the trans concentration. For this special case, flux ratio variations must be due to changes in permeation characteristics of the layer overlying the capillaries (i.e. epithelium, unstirred fluid layer), while unidirectional flux variations can also be attributed to changes in the absorption site blood flow rate.     

Coupling of Solute and Solvent Flows in Porous Lipid Bilayer Membranes

The present experiments were designed to evaluate coupling of water and nonelectrolyte flows in porous lipid bilayer membranes (i.e., in the presence of amphotericin B) in series with unstirred layers. Alterations in solute flux during osmosis, with respect to the flux in the absence of net water flow, could be related to two factors: first, changes in the diffusional component of solute flux referable to variations in solute concentrations at the membrane interfaces produced by osmotic flow through the unstirred layers; and second, coupling of solute and solvent flows within the membrane phase. Osmotic water flow in the same direction as solute flow increased substantially the net fluxes of glycerol and erythritol through the membranes, while osmotic flow in the opposite direction to glycerol flow reduced the net flux of that solute. The observed effects of osmotic water flow on the fluxes of these solutes were in reasonable agreement with predictions based on a model for coupling of solute and solvent flows within the membrane phase, and considerably in excess of the prediction for a diffusion process alone.     

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.     

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.     

The role of microtubules and microfilaments in the hydrosmotic response to antidiuretic hormone

To test the effects of colchicine and cytochalasin B on the ADH-induced response, unidirectional and net water fluxes were measured at one or two minutes intervals in frog urinary bladder. The action of these agents on the appearance of intramembrane particles aggregates in the luminal membrane of target cells under oxytocin stimulation and the changes in the tissue ultrastructure induced by cytochalasin B were also studied. It was observed that: the time-course of the response to oxytocin was strongly slowed by colchicine while the washout was not affected; the time-course of the 'on and off' of the response to oxytocin was not modified by cytochalasin B; cytochalasin B pretreatment proportionally reduced unidirectional and net water fluxes measured after glutaraldehyde fixation; the combined action of colchicine and cytochalasin B proportionally reduced the net water flux and the number of intramembrane particles aggregates, observed in freeze-fracture studies; after cytochalasin B action the dilation of intercellular spaces classically observed under oxytocin stimulation is strongly reduced. It is concluded that: microtubules probably play an important role in the water channels plug-in, but not in their removal; microfilaments integrity is necessary for the mechanisms inducing intercellular space dilation and the observed results confirm that water permeability is controlled by the number of permeation units present in the luminal border of granular cells and probably represented by the intramembrane particle aggregates.     

Cation flux in the ehrlich ascites tumor cell. Evidence for Na+-for-Na+ and K+-for-K+ exchange diffusion.

In a previous study, evidence was presented for an external Na+-dependent, ouabain-insensitive component of Na+ efflux and an external K+-dependent component of K+ efflux in the Ehrlich ascites tumor cell. Evidence is now presented that these components are inhibited by the diuretic furosemide and that under conditions of normal extracellular Na+ and K+ they represent Na+-for-Na+ and K-+for-K+ exchange mechanisms. Using 86Rb to monitor K+ movements, furosemide is shown to inhibit an ouabain-insensitive component of Rb+ influx and a component of Rb+ efflux, both representing approx. 30 percent of the total flux. Inhibition of Rb+ efflux is greatly reduced by removal of extracellular K+. Furosemide does not alter steady-state levels of intracellular K+ and it does not prevent cells depleted of K+ by incubation in the cold from regaining K+ upon warming. Using 22Na to monitor Na+ movements, furosemide is shown to inhibit an ouabain-insensitive component of unidirectional Na+ efflux which represents approx. 22 percent of total Na+ efflux. Furosemide does not alter steady-state levels of intracellular Na+ and does not prevent removal of intracellular Na+ upon warming from cells loaded with Na+ by preincubation in the cold. The ability of furosemide to affect unidirectional Na+ and K+ fluxes but not net fluxes is consistent with the conclusion that these components of cation movement across the cell membrane represent one-for-one exchange mechanisms. Data are also presented which demonstrate that the uptake of alpha-aminoisobutyrate is not affected by furosemide. This indicates that these components of cation flux are not directly involved in the Na+-dependent amino acid transport system A.     

Decrease of transport of some polyols in sickle cells

This paper reports the results of kinetic studies on the inward net-flux of small non-electrolytes (ethylene glycol, glycerol and erythritol) in sickle cells as compared to normal erythrocytes. Net transport rates were evaluated by turbidimetric measurements for ethylene glycol and glycerol and by hematocrit monitoring for erythritol. A 2-fold and 4-fold reduction in the permeability coefficient for ethylene glycol and glycerol, respectively, were found in sickle cells as compared to normal erythrocytes. In contrast, no significant changes in erythritol transport kinetics were observed. The dependence of glycerol permeability on temperature, pH and oxygenation is the same in both types of cells. A significant correlation was observed between glycerol permeability and cell density only for sickle cells. The results indicate that irreversible modifications of membrane proteins, responsible for the glycerol and ethylene glycol transport, do occur in sickle cells.     

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.     

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 bathing 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 Cl^? were increased. The movement of Cl^? was evaluated by comparison of Cl^? 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 on Na⁺ transport.     

Ion Transport in Isolated Rabbit Ileum : I. Short-circuit current and Na fluxes

The transmural potential difference, short-circuit current, and Na fluxes have been investigated in an in vitro preparation of isolated rabbit ileum. When the tissue is perfused with a physiological buffer, the serosal surface is electrically positive with respect to the mucosal surface and the initial potential difference in the presence of glucose averages 9 mv. Unidirectional and net Na fluxes have been determined under a variety of conditions, and in each instance, most if not all of the simultaneously measured short-circuit current could be attributed to the active transport of Na from mucosa to serosa. Active Na transport is dependent upon the presence of intact aerobic metabolic pathways and is inhibited by low concentrations of ouabain in the serosal medium. A method is described for determining whether a unidirectional ionic flux is the result of passive diffusion alone, in the presence of active transport of that ion in the opposite direction. Using this method we have demonstrated that the serosa-to-mucosa flux of Na may be attributed to passive diffusion with no evidence for the presence of carrier-mediated exchange diffusion or the influence of solvent-drag.     

Taurine secretion in primary monolayer cultures of flounder renal epithelium: stimulation by low osmolality

Transepithelial taurine fluxes determined in short-circuited monolayer cultures of flounder renal proximal cells in Ussing chambers revealed net taurine secretion. Both unidirectional secretory and reabsorptive taurine fluxes exhibited saturation kinetics contributed by two distinct saturable transepithelial taurine transport systems operating at different taurine concentration ranges. The taurine secretory system operating below 0. 5 mM had lower affinity but higher capacity than the reabsorptive system, whereas the one operating at high concentrations (0.5-3.0 mM) had higher affinity but the same capacity as the corresponding reabsorptive system. Exposure (2 h) of the cultures to hyposmotic medium in the presence of taurine increased taurine secretory flux twofold with no effect on the reabsorptive flux. The hyposmolality-induced increase in taurine secretion was associated with a decreased peritubular taurine efflux and a concurrent increased luminal taurine efflux; the latter occurred via a pathway that was not affected by 4,4'-diisothiocyanostilbene-2,2'-disulfonic acid but inhibited by probenecid. The culture response in hyposmotic medium mimics the in vivo response of the intact marine fish kidney to dilution.     

Polyol permeability of the human red cell. Interpretation of glucose transport in terms of a pore

The kinetic equations describing transport through a pore that has a binding site and that undergoes a conformational change are identical to those of a carrier model. Therefore, in order to distinguish between the two models it is necessary to test specific predictions based on detailed mechanistic models. A pore model is described in which the substrate (glucose) is able to reach the single binding site only from the outside when the pore is in conformation I and only from the inside when it is conformation II. On the basis of this model it is predicted that solutes which do not have any specific affinity for the binding site should still have a finite permeability via the glucose transport system if they are the same size or smaller than glucose. This permeability should be proportional to the volume of distribution of the solute in the pore and should therefore decrease with increasing molecular size. A geometric pore volume can be estimated from this size dependence. In order to test these predictions, the glucose-dependent permeability of a series of 4-carbon (erythritol), 5-carbon (d-arabitol, l-arabitol and xylitol) and 6-carbon (d-mannitol, d-sorbitol and $\text{myo-}\text{inositol}$) polyols was measured. The permeability of all the polyols is decreased by the presence of glucose and the $\text{K}{}_{\mathrm{<mtext>I</mtext>}}$ of this “inhibitable” component is similar to that of d-sorbose, suggesting that this component is associated with the glucose transport system. Since these observations could be explained entirely in terms of a specific affinity for a carrier binding site, they do not exclude a carrier mechanism. However, as predicted for the pore model, this “inhibitable” permeability decreased with increasing molecular size and the calculated geometric pore volume was of a size that would be expected for a cell membrane pore.     

High- and Low-Affinity Transport of D-Glucose from Blood to Brain

Abstract: Measurements of the unidirectional blood-brain glucose flux in rat were incompatible with a single set of kinetic constants for transendothelial transport. At least two transfer mechanisms were present: a high-affinity, low-capacity system, and a low-affinity, high-capacity system. The low-affinity system did not represent passive diffusion because it distinguished between D-and L-glucose. The T_max and K _m, for the high-affinity system were 0.16 mmol 100 g⁻¹ min⁻¹ and 1 mM; for the low-affinity system, ∼ 5 mmol 100 g⁻¹ min⁻¹ and ∼ 1 M. With these values, physiological glucose concentrations were not sufficient to saturate the low-affinity system. In normoglycemia, therefore, three independent pathways of glucose transport from blood to brain appear to exist: a high-affinity facilitated diffusion pathway of apparent permeability 235·10⁻⁷ cm s⁻¹, a specific but nonsaturable diffusion pathway of permeability 85·10⁻⁷ cm s^−l, and a nonspecifc passive diffusion pathway of permeability 2·10⁻⁷ cm s⁻¹.     

Computer simulation of single-file transport

A stochastic model of single-file transport was developed as the Markov process in continuous time technique. The model was constructed using an EC-1060 computer. Unidirectional fluxes were investigated and populations of channels were correlated with flux fluctuations. The profiles of channel populations were shown to have nonlinear shapes even with the transport of nonelectrolyte (the classical diffusion approach gives linear profiles). The relationship between the paired correlation function F(AB) and the concentration of transported particles was examined. The F(AB) profile was shown to become flattened (or exponential for asymmetrical cases) at high concentrations. The concentration dependence jA/jA0 ratio were analyzed, where jA is a single-file unidirectional flux, jA0 is unidirectional flux for the case of free diffusion. An interesting "stack" phenomenon was observed for abnormal time correlations of single-file fluxes.     

The inhibitory effect of strophanthidin on secretion by the isolated gastric mucosa

The unidirectional fluxes of Na⁺ and Cl^- were measured across the isolated gastric mucosa of the bullfrog (R. catesbiana). The addition of strophanthidin, a cardiac aglycone, resulted in marked reductions of the spontaneous potential and short-circuit current. Associated with these changes, the isolated gastric mucosa ceased secreting chloride and hydrogen ion. Although the active component of chloride transfer was inhibited, the exchange diffusion component seemed to increase. No significant changes in membrane conductance or sodium flux were noted. Possible mechanisms of strophanthidin inhibition were discussed in view of its effect on chloride transport across the gastric mucosa and on sodium and potassium transfer in other tissues. It was concluded that the cardiac glycosides may not be specific inhibitors of sodium and potassium transport. This non-specific inhibition suggests that active chloride transport is affected by strophanthidin directly and/or anion secretion is dependent upon normal functioning of cation transport systems in the tissue.     

Erythritol metabolism in wild-type and mutant strains of Schizophyllum commune

Erythritol uptake and metabolism were compared in wild-type mycelium and a dome morphological mutant of the wood-rotting mushroom Schizophyllum commune. Wild-type mycelium utilized glucose, certain hexitols, and pentitols including ribitol, as well as d-erythrose, erythritol, and glycerol as sole carbon sources for growth. The dome mutant utilized all of these compounds except d-erythrose and erythritol. Erythritol- or glycerol-grown wild-type mycelium incorporated erythritol into various cellular constituents, whereas glucose-grown cells lagged considerably before initiation of erythritol uptake. This acquisition was inhibited by cycloheximide. Dome mycelium showed behavior similar to wild-type in uptake of erythritol after growth on glucose or glycerol, except that erythritol was not further catabolized. Enzymes of carbohydrate metabolism were compared in cell extracts of glucose-cultured wild-type mycelium and dome. Enzymes of hexose monophosphate catabolism, nicotinamide adenine dinucleotide (NAD)-dependent sugar alcohol dehydrogenases, and reduced nicotinamide adenine dinucleotide phosphate (NADPH)-coupled erythrose reductase were demonstrated in both. The occurrence of erythrose reductase was unaffected by the nature of the growth carbon source, showed optimal activity at pH 7, and generated NAD phosphate and erythritol as products of the reaction. Glycerol-, d-erythrose-, or erythritol-grown wild-type mycelium contained an NAD-dependent erythritol dehydrogenase absent in glucose cells. Erythritol dehydrogenase activity was optimal at pH 8.8 and produced erythrulose during NAD reduction. Glycerol-growth of dome mycelium induced the erythritol uptake system, but a functional erythritol dehydrogenase could not be demonstrated. Neither wild-type nor dome mycelium produced erythritol dehydrogenase during growth on ribitol. Erythritol metabolism in wild-type cells of S. commune, therefore, involves an NADPH-dependent reduction of d-erythrose to produce erythritol, followed by induction of an NAD-coupled erythritol dehydrogenase to form erythrulose. A deficiency in erythritol dehydrogenase rather than permeability barriers explains why dome cannot employ erythritol as sole carbon source for mycelial growth.     

The relationship between anion exchange and net anion flow across the human red blood cell membrane

The conductive (net) anion permeability of human red blood cells was determined from net KCl or K2SO4 effluxes into low K+ media at high valinomycin concentrations, conditions under which the salt efflux is limited primarily by the net anion permeability. Disulfonic stilbenes, inhibitors of anion exchange, also inhibited KCl or K2SO4 efflux under these conditions, but were less effective at lower valinomycin concentrations where K+ permeability is the primary limiting factor. Various concentrations of 4,4'-diisothiocyanostilbene-2,2'-disulfonate (DIDS) had similar inhibitory effects on net and exchange sulfate fluxes, both of which were almost completely DIDS sensitive. In the case of Cl-, a high correlation was also found between inhibition of net and exchange fluxes, but in this case about 35% of the net flux was insensitive to DIDS. The net and exchange transport processes differed strikingly in their anion selectivity. Net chloride permeability was only four times as high as net sulfate permeability, whereas chloride exchange is over 10,000 times faster than sulfate exchange. Net OH-permeability, determined by an analogous method, was over four orders of magnitude larger than that of Cl-, but was also sensitive to DIDS. These data and others are discussed in terms of the possibility that a common element may be involved in both net and exchange anion transport.     

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.