Deviations from the flux ratio equation for chloride ions in ouabain- and acetazolamide-treated frog skin.

In order to establish whether or not chloride ions behave as freely moving particles in "passive", i.e. ouabain- and acetazolamide-treated, frog skin, tracer fluxes of 36Cl-have been measured while a voltage (generally +40 mV, serosal side positive) across the skin was applied. Ussing's flux ratio equation has been used as a criterion for this type of transport. One group of skin samples exhibited significant exchange diffusion phenomena. Most samples in a second group either behaved according to the flux ratio equation of showed significant and extreme exchange diffusion. From flux ratios obtained at two different voltages across various skin samples, showing extreme exchange diffusion, it appeared that the simple form of Kedem and Essig's law derived from irreversible thermodynamics, which is valid for homogeneous systems, does not apply to the type of exchange diffusion found. The system can, however, be described by a 1:1 exchange mechanism working in parallel with a diffusional pathway. The ratio exchange flux/observed efflux must then have a constant value (0.83) at the voltages appled, which implies that the exchange flux is voltage dependent. By comparison with iodide flux experiments as carried out by Ussing, it is shown that iodide exhibits the same type of exchange diffusion. A carrier, possibly responsible for the observed behaviour, is described.     

The diagram methods for the evaluation of exchange fluxes in membrane transport systems

In this paper theoretical methods for the evaluation of fluxes of ligand exchange processes in a transporter-mediated membrane transport system are studied. The exchange process of a transport system is defined as a set of reactions of the transporters in the membrane that do not result in a complete turnover and must include the following consecutive sequence of steps: the binding of ligands from bath 1 and a subsequent release of bound ligands to bath 2 followed immediately by a binding of ligands from bath 2 and a subsequent release of bound ligands to bath 1. Thus, unlike the ordinary one-way cycles, the completion of an exchange process does not result in a net transport of ligands across the membrane. However, since it exchanges the ligands between the two baths, the exchange process of a transport system is closely related to the operational tracer flux of labelled ligands in the system. In this paper, both the numerical and the analytical procedures for the evaluation of exchange fluxes in any given biochemical diagram are discussed. In particular, we show that the exchange fluxes of a given kinetic diagram, like one-way cycle fluxes, can be expressed analytically in terms of the rate constants of the diagram with the use of either the original diagram or an expanded diagram. The diagram methods presented in this paper should be very useful in analyzing the mechanisms of transporter-mediated transport systems when tracer flux data are available.     

Deviations from the flux ratio equation for chloride ions in ouabain- and acetazolamide-treated frog skin

In order to establish whether or not chloride ions behave as freely moving particles in “passive”, i.e. ouabain-and acetazolamide-treated, frog skin, tracer fluxes of ³⁶Cl⁻ have been measured while a voltage (generally +40 mV, serosal side positive) across the skin was applied. Ussing's flux ratio equation has been used as a criterion for this type of transport. One group of skin samples exhibited significant exchange diffusion phenomena. Most samples in a second group either behaved according to the flux ratio equation or showed significant and extreme exchange diffusion. From flux ratios obtained at two different voltages across various skin samples, showing extreme exchange diffusion, it appeared that the simple form of Kedem and Essig's law derived from irreversible thermodynamics, which is valid for homogeneous systems, does not apply to the type of exchange diffusion found. The system can, however, be described by a 1 : 1 exchange mechanism working in parallel with a diffusional pathway. The ratio exchange flux/observed efflux must then have a constant value (0.83) at the voltages applied, which implies that the exchange flux is voltage dependent. By comparison with iodide flux experiments as carried out by Ussing, it is shown that iodide exhibits the same type of exchange diffusion. A carrier, possibly responsibe for the observed behaviour, is described.     

Colorimetric device for measurement of transvascular fluid flux in blood-perfused organs

The aim of this study was to develop a device capable of measuring transvascular fluid flux in blood-perfused organs. For any given blood flow through the organ (QT), transvascular flux (QF) can be considered as the fraction of QT exchange. Presumably, QF would change the background concentration of an impermeable tracer residing in the perfusate. Thus QF could be calculated from the relative changes in tracer concentration for any given QT. We have used Blue Dextran (1 g/l of blood) as the reference tracer. Because the minimum molecular weight of Blue Dextran is 2 X 10(6), we anticipated it to behave as an impermeable tracer in most organs. QF was simulated with continuous infusions of plasma, normal saline solution, and a 50% mixture of both. Changes in Blue Dextran concentration were continuously followed colorimetrically by changes in transmission of specific light at a wavelength of 632 nm. Because 632-nm light is affected by hematocrit and O2 saturation changes, two additional wavelengths were used: 815-nm, which is not affected by saturation or Blue Dextran concentration changes, was used to account for changes in hematocrit, and 887-nm specific light, which is not affected by Blue Dextran, served to correct for saturation changes. Red cells could not be used as the reference tracer because of the possibility of hematocrit changes independent of fluid flux (Fahraeus effect). The device so constructed proved capable of measuring rates of fluid infusion in the order of 0.1% of QT with a variability of 10% around the mean.     

The thermodynamic meaning of metabolic exchange fluxes

Metabolic flux analysis (MFA) deals with the experimental determination of steady-state fluxes in metabolic networks. An important feature of the ¹³C MFA method is its capability to generate information on both directions of bidirectional reaction steps given by exchange fluxes. The biological interpretation of these exchange fluxes and their relation to thermodynamic properties of the respective reaction steps has never been systematically investigated. As a central result, it is shown here that for a general class of enzyme reaction mechanisms the quotients of net and exchange fluxes measured by ¹³C MFA are coupled to Gibbs energies of the reaction steps. To establish this relation the concept of apparent flux ratios of enzymatic isotope-labeling networks is introduced and some computing rules for these flux ratios are given. Application of these rules reveals a conceptional pitfall of ¹³C MFA, which is the inherent dependency of measured exchange fluxes on the chosen tracer atom. However, it is shown that this effect can be neglected for typical biochemical reaction steps under physiological conditions. In this situation, the central result can be formulated as a two-sided inequality relating fluxes, pool sizes, and standard Gibbs energies. This relation has far-reaching consequences for metabolic flux analysis, quantitative metabolomics, and network thermodynamics.     

The face value of ion fluxes: the challenge of determining influx in the low-affinity transport range

The existence of distinct high- and low-affinity transport systems (HATS and LATS) is well established for major nutrient ions. However, influx mediated by these systems is usually estimated using uniformly simple tracer protocols. Two (42)K radiotracer methods to measure potassium influxes in the HATS and LATS ranges in intact barley (Hordeum vulgare L.) roots are compared here: a direct influx (DI) method, and an integrated flux analysis (IFA), which is designed to account for tracer efflux from labelled roots and differential tracer accumulation along the plant axis. Methods showed only minor discrepancies for influx values in the HATS range, but large discrepancies in the LATS range, revealing striking distinctions in the cellular exchange properties dominated by the operation of the two transport systems. It is shown that accepted DI protocols are associated with very large errors in the high-conductance LATS range, underestimating influx at least 6-fold due to four characteristics of this transport mode: (i) accelerated cellular (42)K exchange; (ii) a greatly increased ratio of efflux to influx; (iii) increased (42)K loss during the removal of water from roots in preweighing centrifugation or blotting protocols; and (iv) increased (42)K retention at the root-shoot interface, a region of the plant frequently disregarded in DI determinations. The findings warrant a re-evaluation of a large body of literature reporting influx in the LATS range, and are of fundamental importance to ion flux experimentation in plant physiology.     

Single channel gating events in tracer flux experiments. II. Flux amplitude analysis

Measurement of tracer ion flux from or into a collection of closed membrane structures (CMS) constitutes a broadly applicable technique for studying ion channel gating by specialized gating molecules in biological membranes. The amplitudes for the flux process reflect the overall change in tracer content due to flux during a period in which channels on at least some of the CMS were open. In practice, the attainment of a time-invariant, finite overall tracer content, indicating a cessation of flux, need not imply that flux has reached completion, i.e., that the CMS internal and external tracer concentrations have fully reached equilibrium. Less than maximum flux amplitudes arise when binding of control ligands leads to an inhibition or inactivation of the channel gating molecules prior to a complete equilibration of tracer. Analysis of the dependence of the flux amplitudes on control ligand concentration permits determination of characteristic parameters of the CMS that may vary with the methods of preparation (e.g., the distributions of CMS size and CMS content of gating units). Knowledge of these parameters in turn permits evaluation of the mean single channel flux amplitude contribution, which is functionally dependent on the rate constant ratio (k'eff/ki), where k'eff and ki are, respectively, the effective rate constants for tracer flux and for gating unit inactivation.     

Sulphate supply and its regulation of transport in roots of a tropical legume Macroptilium atropurpureum cv. Sirato

During a period of sulphate deprivation, roots of Macroptiliumatropurpureum responded by increasing their uptake capacityat the plasma membrane. This effect was apparent both in intactplants and in tissues excised prior to uptake. In experiments using excised root systems previousy labelledwith ³⁵SO₄^2- the rate of tracer transport to the xylem was muchgreater in roots subsequently deprived of external sulphatethan in those supplied with unlabelled sulphate. Removing theexternal sulphate to the external solution. Additionally, compartmentalanalysis of tracer exchange kinetics showed that the flux ofsulphate from the cytoplasm to the xylem(     

Rates of exchange of free amino acids between plasma and brain in mice

The rate of appearance of label in the brain in mice following the intraperitoneal or intravenous injection of tracer doses of amino acids was measured in short time periods (1–8 min). Amino acid flux varied between 2 and 10 nmol/min per g brain for the amino acids used. Defining half-life as the uptake of labeled amino acid amounting to 50% of endogenous levels, a short half-life (between 3 and 30 min) was found for the essential amino acids. The half-life of the nonessential amino acids varied between 2 and 24 h, depending on their level in brain. Flux (exchange) of an amino acid was increased when the level of amino acids belonging to the same transport class was increased by intracerebral injection. Protein-free diet resulted in decrease in some amino acids, increase in others; flux was altered parallel to changes in brain levels in animals on this diet. The stercospecificity of exchange and the substrate specificity of effects of altered brain amino acids indicate that exchange occurs via mediated transport. Mediated exchange was present in immature brain. Heteroexchange (flow of one amino acid causing the counterflow of a related amino acid) may play an important part in cerebral homeostasis.     

Transient transcapillary exchange of water driven by osmotic forces in the heart

Osmotic transient responses in organ weight after changes in perfusate osmolarity have implied steric hindrance to small-molecule transcapillary exchange, but tracer methods do not. We obtained osmotic weight transient data in isolated, Ringer-perfused rabbit hearts with NaCl, urea, glucose, sucrose, raffinose, inulin, and albumin and analyzed the data with a new anatomically and physicochemically based model accounting for 1) transendothelial water flux, 2) two sizes of porous passages across the capillary wall, 3) axial intracapillary concentration gradients, and 4) water fluxes between myocytes and interstitium. During steady-state conditions approximately 28% of the transcapillary water flux going to form lymph was through the endothelial cell membranes [capillary hydraulic conductivity (Lp) = 1.8 +/- 0.6 x 10-8 cm. s-1. mmHg-1], presumably mainly through aquaporin channels. The interendothelial clefts (with Lp = 4.4 +/- 1.3 x 10-8 cm. s-1. mmHg-1) account for 67% of the water flux; clefts are so wide (equivalent pore radius was 7 +/- 0.2 nm, covering approximately 0.02% of the capillary surface area) that there is no apparent hindrance for molecules as large as raffinose. Infrequent large pores account for the remaining 5% of the flux. During osmotic transients due to 30 mM increases in concentrations of small solutes, the transendothelial water flux was in the opposite direction and almost 800 times as large and was entirely transendothelial because no solute gradient forms across the pores. During albumin transients, gradients persisted for long times because albumin does not permeate small pores; the water fluxes per milliosmolar osmolarity change were 200 times larger than steady-state water flux. The analysis completely reconciles data from osmotic transient, tracer dilution, and lymph sampling techniques.     

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.     

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.     

Single channel gating events in tracer flux experiments I. Theory

Tracer ion flux measurements are a commonly used method for studying ion transport through membranes of cellular systems, where the rate of ion flow is determined by gating processes which control the opening and closing of transmembrane channels. Due to recent advances in the theoretical analysis of tracer flux from or into closed membrane structures (CMS), the mechanism of gating reactions can, in principle, be derived from flux data. A physically well founded analysis is presented for the dependence of the total tracer ion content of a collection of CMS on the gating processes. For functionally uncoupled gating units a mean single channel flux contribution [equation, see text] can be defined, where k is the intrinsic single channel flux coefficient, t the time over which flux is measured, and p(tau,t) is the probability that a given channel was open for a total period tau during t. This quantity reflects the mean time course of the tracer content due to flux through a single channel. Expressions for are derived that explicitly take into account a distribution in the lifetime of open channels. On the basis of the results, kinetic and thermodynamic parameters of multiphasic gating reactions can be determined from the time course of the overall tracer content in a colleciion of CMS.     

Modeling of transendothelial transport

Capillary-tissue exchange of inert hydrophilic solutes in the heart occurs through aqueous channels, the clefts between endothelial cells (ECs). For adenosine (and other vasoactive agents and substrates), there is also transport across the plasmalemma of the ECs. The multiple-indicator dilution technique comparing tracer adenosine flux with that of 9-beta-D-arabinofuranosylhypoxanthine (an analog that is not transported by the nucleoside carrier) can be used to estimate the conductance of the facilitated transport mechanism, which is equivalent to a permeability-surface area product. Analysis by using a model of exchanges among capillary, EC, interstitium, and myocardial cells suggests that the abluminal surface of the ECs is also highly permeable to adenosine. The inference is that ECs may be an important component of a system for adenosine exchange and regulation in the heart.     

A new, non-perturbing, sampling procedure in tracer exchange measurements

An isotope procedure for the tracing of ion fluxes and rate constants in intact plants is presented and applied to 42K-labelled potassium fluxes in cells of intact barley (Hordeum vulgare L.) roots. This procedure differs from conventional tracer efflux protocols in that tracer accrual in the external solution bathing the labelled roots is continually monitored by solution subsampling, whereas conventional protocols involve monitoring the specific-activity decline in a sequence of eluates that wash out tracer released by roots. The new technique minimizes physical disturbance to the plant system, while permitting excellent time resolution of efflux kinetics. In the high-affinity transport (HATS) range, the flux and exchange parameters determined using this method showed close agreement with those found using a conventional protocol. However, in the low-affinity transport (LATS) range, substantially higher influx and efflux were seen than are normally observed with conventional tracer techniques. It is shown that this difference is attributable to the greater disturbance-sensitivity of LATS transport, and conclude that the measurement of fluxes is much more difficult in this transport range than in the disturbance-resistant HATS range.     

Modeling flux of free and protein-bound radioisotopes into the pulmonary interstitium

Several groups of investigators are using external detection of radiolabeled protein to study the flux of protein from plasma into the pulmonary interstitium. A basic assumption for these studies has been that the unbound (free) tracer concentration is small and insignificant. The purpose of this study is to evaluate how free tracer influences the determination of normalized slope index. A five-compartment model for the lung was used with transport equations for both unbound and bound nuclide flux. Parameters of the unbound and bound transport equations were varied to evaluate the sensitivity of normalized slope index to each parameter. The model was also compared with published protein flux data to investigate the validity of the transport model. Application of the model to external scan data provides a sensitive method for evaluating the flux of bound and unbound tracers into the pulmonary interstitium. We conclude that because the distribution volume for unbound tracer is large with respect to protein distribution volume, even a small amount of unbound tracer (2-5%) can create large errors in the determination of normalized slope index.     

Regulation of Na+-H+ exchange in cultured opossum kidney cells by parathyroid hormone, atrial natriuretic peptide and cyclic nucleotides

The activity of Na+-H+, exchange was studied in a cultured cell line derived from opossum kidney (OK cells). The activity of the exchanger was measured either as the amiloride (2 mM) inhibitable 22Na flux in acid-loaded cells, or as the Na+-dependent and amiloride-sensitive recovery of intracellular pH (pHi) from an acid load. Initial rates of tracer flux were analyzed in confluent monolayers while changes in pHi were evaluated in suspensions of trypsinized cells which had been loaded with 2',7'-bis(2-carboxyethyl)-5,6-carboxyfluorescein. Both 8-bromo-cAMP and 8-bromo-cGMP inhibit the activity of the exchanger in a dose-dependent manner. Maximal inhibition due to 8-bromo-cAMP was about 50% and was attained with 0.75 mM of the cyclic nucleotide. Parathyroid hormone (10(-9)-10(-7) M) and atrial natriuretic peptide (10(-7) M) also inhibit the activity of the exchanger. By measuring the rate of Na+-dependent pHi recovery from different starting pHi values, evidence was obtained for a cyclic nucleotide-dependent decrease in the response of Na+-H+ exchange to intracellular acidification. We conclude that cAMP and cGMP are intracellular messengers in the hormone-dependent regulation of Na+-H+ exchange activity in renal epithelial cells.     

Steady State Sodium and Rubidium Effluxes in Pisum sativum Roots

Steady state effluxes of potassium and sodium ions were measured on Pisum sativum var. Alaska root segments excised from seedlings which had grown in a nutrient solution containing the major inorganic ions and either ⁸⁶Rb as a tracer for K or ²²Na as a tracer for Na. Fluxes appeared to be from 2 cellular compartments, a small compartment with a high flux rate and a larger compartment with a slow flux rate. Cell wall exchange fluxes are believed to have been negligible. Efflux rates for 11.3% and 88.7% of cellular potassium ions were 6 × 10⁻⁷ and 1.32 × 10⁻⁷ respectively; rates for 33.7% and 66.3% of cellular sodium ions were 1.48 × 10⁻⁷ and 3.83 × 10⁻⁸ respectively, (equivalents per gram fr wt per hr). The sodium flux measurements, with previous measurements of ionic concentrations and transmembrane potentials, support the theory that sodium is transported actively from Pisum roots.     

Elevated TCA cycle function in the pathology of diet-induced hepatic insulin resistance and fatty liver

The manner in which insulin resistance impinges on hepatic mitochondrial function is complex. Although liver insulin resistance is associated with respiratory dysfunction, the effect on fat oxidation remains controversial, and biosynthetic pathways that traverse mitochondria are actually increased. The tricarboxylic acid (TCA) cycle is the site of terminal fat oxidation, chief source of electrons for respiration, and a metabolic progenitor of gluconeogenesis. Therefore, we tested whether insulin resistance promotes hepatic TCA cycle flux in mice progressing to insulin resistance and fatty liver on a high-fat diet (HFD) for 32 weeks using standard biomolecular and in vivo (2)H/(13)C tracer methods. Relative mitochondrial content increased, but respiratory efficiency declined by 32 weeks of HFD. Fasting ketogenesis became unresponsive to feeding or insulin clamp, indicating blunted but constitutively active mitochondrial β-oxidation. Impaired insulin signaling was marked by elevated in vivo gluconeogenesis and anaplerotic and oxidative TCA cycle flux. The induction of TCA cycle function corresponded to the development of mitochondrial respiratory dysfunction, hepatic oxidative stress, and inflammation. Thus, the hepatic TCA cycle appears to enable mitochondrial dysfunction during insulin resistance by increasing electron deposition into an inefficient respiratory chain prone to reactive oxygen species production and by providing mitochondria-derived substrate for elevated gluconeogenesis.     

86Rb+ fluxes in Chinese hamster ovary cells as a function of membrane cholesterol content

Steady-state fluxes of 86Rb+ (as a tracer for K+) were measured in Chinese hamster ovary cells (CHO-K1) and a mutant (CR1) defective in the regulation of cholesterol biosynthesis; the membrane cholesterol content of this mutant was varied by growing it on a range of cholesterol supplements to lipid-free medium (Sinensky, M. (1978) Proc. Natl. Acad. Sci. U.S. 75, 1247--1249). Analogous to previous findings in ascites tumor cells, 86Rb+ influx in the parent strain was differentiated into a ouabain-inhibitable 'pump' flux, furosemide-sensitive, chloride-dependent exchange diffusion, and a residual 'leak' flux. On the basis of this flux characterization, 86Rb+ pump and leak fluxes were measured in the mutant as a function of membrane cholesterol content. Pump and leak fluxes, when expressed per ml cell water, were independent of the cholesterol content of the mutant. Moreover, 86Rb+ fluxes in the mutant were equal to those in the parent strain. Our data imply that the flux behavior of K+ in the steady state is independent of the ordering of membrane lipid acyl chains.