Energetics of sodium transport in frog skin. II. The effects of electrical potential on oxygen consumption

What process is glycolytic stoichiometry optimal for?

It has been proposed that the glycolytic stoichiometry of 2 ATP per glucose is the result of an optimization that maximizes the rate of ATP production. However, using a nonequilibrium thermodynamic approach, we show here that glycolysis operates under optimal output power and not at optimal flow of ATP production. Furthermore, it can be proved that the same maximal output power can be achieved with different stoichiometries. However, changes in the glycolytic stoichiometry would dramatically affect the efficiency of all those cellular processes powered by ATP. Our results suggest that the stoichiometric coefficient, as found in most contemporary cells, may be the outcome of an evolutionary process leading to yield an operative quantum energy for the hydrolysis of ATP.

The ATP paradox is the expression of an economizing fuel mechanism

The strong negative correlation between glycolytic flux and intracellular ATP concentration observed in yeast has long been an intriguing and counterintuitive phenomenon, which has been referred to as the ATP paradox. Herein, using principles of irreversible thermodynamics it was shown that if the ATP-consuming pathways are more sensitive to extracellular glucose than glycolysis, then upon glucose addition glycolysis performance can switch from an efficient working regime to a dissipative regime, and vice versa, depending on glucose availability. The efficient regime represents a good compromise between high output power and low dissipation, whereas the dissipative working regime offers a higher output power although at a high glucose cost. The physiological and evolutionary implications of this switch strategy are discussed.

Effect of norepinephrine on renal tubular Na-K-ATPase and oxygen consumption

Previous studies from this laboratory have demonstrated that norepinephrine (NE) increases sodium dependent phenylalanine uptake by in vitro rat cortical tubules. In the present study, we have examined whether the observed increase in proximal tubular sodium transport, during NE treatment, is related to changes in membrane Na-K-ATPase and cellular oxygen consumption. Treatment of intact tubules with NE increased microsomal Na-K-ATPase activity but had no effect on cellular oxygen consumption or ouabain inhibitable oxygen consumption. The increased Na-K-ATPase activity is consistent with the observed increase in sodium transport while the lack of a detectable effect on oxygen consumption suggests that the increased transport does not require additional oxygen utilization.

The amiloride-sensitive sodium channel

Net Na+ movement across the apical membrane of high-electrical resistance epithelia is driven by the electrochemical potential energy gradient. This entry pathway is rate limiting for transepithelial transport, occurs via a channel-type mechanism, and is specifically inhibited by the diuretic drug amiloride. This channel is selective for Na+, Li+, and H+, saturates with increasing extracellular Na+ concentration, and is not affected, at least in frog skin epithelium, by changes in apical membrane surface potential. There also appears to be multiple inhibitory regions associated with each Na+ channel. We discuss the possible implications of a voltage-dependent block by amiloride in terms of macroscopic inhibitory phenomena. We describe the use of cultured epithelial systems, in particular, the toad kidney-derived A6 cell line, and the preparation of apical plasma membrane vesicles to study the Na+ entry process. We discuss experiments in which single, amiloride-sensitive channel activity has been detected and summarize current experimental approaches directed at the biochemical identification of this ubiquitous Na+ transport system.

The significance of changes in thermodynamic affinity induced by aldosterone in sodium-transporting epithelia

The energetics of sodium transport were examined in toad (and occasionally frog) skin, with particular emphasis on the effect of aldosterone. Thermodynamic affinity was computed according to Essig and Caplan. Following treatment with antidiuretic hormone or drugs believed to affect only the apical membrane barrier, no change in thermodynamic affinity was observed either acutely (after one to two hours) or chronically (after 18-odd hours hours). By contrast, following treatment with aldosterone overnight, thermodynamic affinity was considerably increased, whether or not incubation was conducted in the presence of sodium in the outer solution; addition of glucose at the end of incubation, whereby sodium transport was stimulated further, failed to influence affinity as measured. The stoichiometry between sodium transport and oxygen consumption was, however, unchanged by aldosterone treatment in short-circuit conditions, neither was that fraction of aerobic metabolism unrelated to sodium transport influenced. It is concluded that the change observed with aldosterone can be directly ascribed to the hormone, as it is independent of glucose availability and of sodium transport. Aldosterone action, at least following prolonged incubation, therefore does not involve only an increase in apical conductance for sodium.

Relationship of transepithelial electrical potential to membrane potentials and conductance ratios in frog skin

Previous studies in anuran epithelia have shown that, after clamping the transepithelial voltage in symmetrical sequences for 4-6 min there is near-constancy of the rate of active Na transport and the associated oxidative metabolism, with a near-linear potential dependence of both. Here we have investigated in frog skin the cellular electrophysiolgical events associated with voltage clamping (Vt = inside-outside potential). Increase and decrease of Vt produced converse effects, related directly to the magnitude of Vt. Hyperpolarization resulted in prompt decrease in inward transepithelial current It and increase in fractional outer membrane resistance fRo (as evaluated from small transient voltage perturbations) and in outer membrane potential Vo. Overshoot of Vo was followed by relaxation to a quasi-steady state in minutes. Changes in fRo were progressive, with half times of some 1-5 sec. Changes in transepithelial slope conductance gt were more variable, usually preventing precise evaluation of the outer and inner cell membrane conductances go and gi. Nevertheless, it was shown that go is related inversely to Vt and Vo. Presuming insensitivity of gi to Vt, the dependence of Go on Vo in the steady state much exceeds that predicted by the constant field equation. Apparent inconsistencies with earlier results of others may be attributable to differences in protocol and the complex dependence of go on Vo and/or cellular-current. In contrast to previous findings in tight epithelia at open circuit, differences in Vt were associated with substantial differences in fRo and inner membrane potential Vi. Hyperpolarization of Vt over ranges commonly employed in studies of active transport ad metabolism appears to increase significantly the electrochemical work per Na ion transported.

Intra- and transepithelial analytical techniques

Epithelia transport a variety of solutes and water. Study of such transport requires a determination of the driving forces responsible for transport, of the pathways through which transport occurs, and of the factors controlling such transport. Transepithelial driving forces are readily determined where the composition of the bathing media can be altered and electrical forces negated. Where substances move only through a paracellular pathway such manipulations may be adequate to define the permeability and selectivity of the pathways. For substances utilizing a cellular pathway, driving forces and permeabilities across the two dissimilar apical and basolateral cellular membranes must be determined. Where a substance can be shown to move across a membrane against its electrochemical potential gradient, the source of the energy for such movement must be assessed. This review focuses on the applicability and validity of a variety of techniques utilized for the study of epithelial transport to answer these questions. These include microelectrode techniques, chemical analyses, microprobe analysis, microscopy, and techniques for assessing the coupling of metabolism to transport.

Effects of antidiuretic hormone on kinetic and energetic determinants of active sodium transport in frog skin

The effects of antidiuretic hormone (ADH) on the rate of transepithelial active Na transport JaNa and the rate of suprabasal O2 consumption of Jsbr were studied in paired hemiskins of frog. Within some 30 min following administration of ADH both JaNa and Jsbr increased to near-maximal levels and then remained stable for at least an hour. On symmetric perturbation of the transepithelial electrical potential delta psi at 6-min intervals, the dependence of JaNa and Jsbr on delta psi was near-linear, both in control and experimental hemi-skins. The stability and near-linearity of the system permitted systematic analysis of the parameters of linear non-equilibrium thermodynamic (NET) and electrical equivalent circuit (EC) formulations. ADH (100 mU/ml) stimulated two of the three NET phenomenological L coefficients, as well as A, the affinity (negative Gibbs free energy) of a metabolic reaction driving transport. Observations at partially depressed levels of transport indicated that the effects of kinetic and energetic factors are to some extent discrete. EC analysis showed stimulation of the amiloride-sensitive conductance Ka, but not of the apparent electromitive force of Na transport 'ENa'. Similar effects were produced by 10 mU/ml of ADH or by 10 mM dibutyryl cyclic AMP, although less marked effects on the L coefficients were noted with the lower concentration of hormone. It is suggested that, in contrast to EC analysis, the NET formulation distinguishes between kinetic and energetic determinants of transport, supporting a dual mechanism of action of ADH.

Time course of active Na transport and oxidative metabolism following transepithelial potential perturbation in toad urinary bladder

The use of an Ussing chamber with well-defined mixing characteristics coupled to a mass spectrometer permits the concurrent evaluation of transepithelial current and oxidative metabolism with improved temporal resolution. The time-course of the amiloride-sensitive current Ia and the rate of suprabasal CO2 production JsbCO2 were observed in 10 toad urinary bladders at short-circuit and after clamping delta psi at 100 mV, serosa positive. Following perturbation of delta psi (0 leads to 100 mV), Ia declined sharply within 1/2 min, remaining near constant approximately 15 min, and then increased slightly. JsbCO2 declined more gradually, remained near constant at approximately 4-7 min, and then declined further. Detailed analysis revealed an early quasi-steady state with near constancy of JsbCO2 starting at 2.9 +/- 1.1 (SD) min and lasting 4.7 +/- 1.8 (SD) min, followed by relaxation to a later steady state at about 15 min. During the early quasi-steady state, Ia was also nearly constant. Considering that in steady states Ia/F approximately or equal to JaNa, the rate of transepithelial active Na transport, during the early quasi-steady state mean values +/- SE of JaNa, JsbCO2 and (JaNa/JsbCO2) were, respectively, 29.9 +/- 1.7%, 59.4 +/- 3.2%, and 56.4 +/- 5.7% of values at short-circuit. Corresponding values during the late steady state were 41.4 +/- 6.0%, 38.2 +/- 6.1%, and 111.3 +/- 8.6%. Thus the flow ratio JaNa/JsbCO2 was depressed significantly during the early quasi-steady state, but returned later to the original value. The results of measurements of Ia and JsbO2 in three hemibladders were qualitatively similar. In terms of a phenomenological "black-box" treatment the findings are consistent with earlier studies indicating incomplete coupling between transport and metabolism. Further studies will be required to clarify the molecular basis for these observations.

Protocol-dependence of equivalent circuit parameters of toad urinary bladder

Determinations o- current-voltage relationships are widely employed in the characterization of epithelial sodium transport. In order to determine the protocol dependence of transport parameters in the toad urinary bladder, studies were carried out in the presence and absence of amiloride, an inhibitor of active sodium transport. With symmetric positive and negative perturbations of the transepithelial electrical potential difference delta psi (0 leads to +/- 100 mV) for 30 sec, the amiloride-sensitive current-voltage (ia-delta psi) relationship was near linear over the range -75 leads to +100 mV, indicating constancy of the conductance ka and the apparent electromotive force "ENa", lumped parameters of the standard electrical equivalent circuit model of the active transport system. With a reverse protocol (+/- 100 leads to 0 mV) or 15 min perturbations the ia-delta psi relationships were highly nonlinear. Nonlinearity reflected voltage dependence of parameters: perturbations that increased active transport decreased "ENa" and increased ka, as evaluated from 10 sec perturbations of delta psi; slowing of active transport produced the converse changes. These effects are usefully analyzed in both quasi-steady states and true steady states by means of a detailed equivalent circuit incorporating the significant ionic currents across each plasma membrane. Precise understanding of the significance of ka and "ENa" will require characterization of the partial ionic conductances on perturbation of delta psi.

Voltage-current relation and K+ transport in tobacco hornworm (Manduca sexta) midgut

Voltage-current curves for the isolated midgut of the tobacco hornworm were determined by transient and steady voltage clamping over the range of 200 to -200 mV. Over this range the transient method yields a linear relation while the steady method usually yields a curve consisting of two lines of differing slope which intersect at zero voltage. The difference between the results of the methods is due to a slow decline in total conductance which accompanies steady voltage clamping. Holding the midgut at short circuit increases the total conductance of the tissue in a manner consistent with increasing shunt conductance; this effect was seen in both diet-reared and leaf-reared animals. When potassium transport is inhibited by substitution of choline or sodium for potassium in bathing solution the total conductance decreases and the voltage-current curve intersects the normal curve in the hyperpolarizing region. Applying a simple equivalent circuit analysis to the results from partial or total potassium replacement suggests that the electromotive force of the potassium transport system is of the order of 140-190 mV. The conductance decrease during inhibition of potassium transport by transient anoxia is of similar magnitude, suggesting that a major effect of metabolic inhibition is to decrease the active conductance of the potassium transport pathway.

Effect of amiloride on conductance of toad urinary bladder

The transepithelial conductance of toad bladder epithelia and the amplitude of the fluctuations of this conductance caused by the action of the underlying smooth muscle have been further investigated. In particular, amiloride was found to reduce both tissue conductance and its fluctuating component to the same extent. Analysis suggests that the steady-state conductance of the toad urinary bladder may be associated only with the paracellular pathway for ions.

Simulation of coupling between chemical reactions and ion transport in brown adipose tissue using network thermodynamics

Several cellular events associated with energy turnover in the mitochondria and at the Na+/K+ plasma membrane pump have been formulated in terms of network thermodynamics. The calorigenic role of the Na+/K+ pump is examined in terms of the relationship between the movement of sodium and potassium ions and the chemical reactions involved. In addition, attention is centered on the potential thermogenic role of three mitochondrial pathways involving proton fluxes--namely, one in which protons are transported from the matrix to the intermembrane space; a second in which protons are transferred back into the matrix in conjunction with the synthesis of ATP; and a third wherein protons re-enter the matrix without being coupled to any chemical reaction. (This latter pathway has been delineated by studies on isolated mitochondria and may be unique to brown fat.) At both sites (plasma membrane and mitochondria) the conversion of chemical energy to heat is considered.

A thermodynamic analysis of the correlation between active Na+ transport and the rate of oxygen consumption in epithelia

Active transport in epithelia is discussed in terms of the relationships between oxygen consumption and sodium flux as affected by each of the two corresponding thermodynamic forces. Analysis is presented of the use of nonequilibrium thermodynamics as a total in elucidating coupling and stoichiometry, and in evaluating drug action in the system. The analysis leads to the quantitative characterization of active transport in "two-flow" systems in terms of two plots: oxygen consumption nad sodium flow, each as a function of electrical potential difference, at constant affinity and constant concentrations. The relevant characteristic parameters are then shown to be represented by the slopes and intercepts of the two plots, the ratios of the slopes and of the intercepts, and by the difference--as well as the ratio--of the ratios. Distinction is made between experimental conditions in which the phenomenological coefficients remain constant and those in which these coefficients undergo appreciable changes. In terms of the above analysis, and examination is made of the effect of commonly used drugs. It is shown that while drugs may effect both the affinity and the phenomenological coefficients, they invariably affect the latter--at least in the cases hitherto reported.

Effects of pH, Ca, ADH, and theophylline on kinetics of Na entry in frog skin

The short circuit current as a function of Na concentration in both solutions was found to obey Michaelis-Menten kinetics under a variety of experimental conditions. Values of maximal transport rate (Im) and half-maximal Na concentrations (Kt) were determined from these experiments. Three type of results were obtained: 1) Im and Kt both decreased by approximately the same fraction when the pH of both solutions was reduced by increasing PCO2, 2) Im decreased and Kt increased when the external pH was decreased, and 3) Im increased with ADH and theophylline, decreased with external Ca, and Kt remained unchanged. Various criteria were utilized to determine that these were properties of the entry barrier for Na into the "transport pool." The results are explained in terms of a model that separates three different types of actions on the entry barrier: 1) competition of Na with other ions in the external solution for entry, 2) modulation of the number of sites available for Na translocation by changing the cytoplasmic pH, and 3) alterations in the rate of Na translocation caused by changes in the Na permeability or the electrochemical gradient across the entry barrier.

Transients in toad skin: short circuit current and ionic fluxes related to inner sodium substitution by monovalent cations

When the Na electrochemical potential difference across the skin (delta muNa) is altered by perturbing the transmembrane electrical potential difference or the external Na concentration, effects on transport and associated oxygen consumption can be described by the formalism of linear nonequilibrium thermodynamics (Vieira, Caplan & Essig, 1972, J. Gen. Physiol. 59:77; Danisi & Lacaz-Vieira, 1974, J. Gen. Physiol. 64:372; Procópio and Lacaz-Vieira, 1977, J. Membrane Biol. 35:219). We now show that with modifications of delta muNa by substitution of Li or choline for Na in the inner bathing solution, this formalism is no longer applicable. Inner Na by K substitution ((Na X K)i) causes profound alterations in short-circuit current (SCC), JinNa, K efflux (JeffK) and PD. SCC drops transiently after (Na X K)i in Cl and in SO4 media, increasing subsequently. In Cl medium, following the initial transient, there is a late decline in SCC toward a steady state. The rate of SCC decline in Cl medium is more pronounced than that observed in SO4 medium. (Na X K)i causes a transient increase in JinNa with a peak synchronous to the minimum in SCC, both in Cl and in SO4 media. This was interpreted as due to depolarization of the inner membrane. In SO4 medium, following the peak observed after (Na X K)i, JimNa drops, to increase again toward a steady state in which SCC and JinNa are not statistically different, resembling the control condition before (Na X K)i. In Cl medium, however, the JinNa steady state is approximately 100% higher than SCC. This difference is due to an important K efflux (JeffK), which builds up progressively after the substitution. The apparent K permeability [JeffK/(Ki)] is of comparable magnitude in Cl and in SO4 media before (Na X K)i and also in SO4 medium after (Na X K)i. However, in Cl medium, after (Na X K)i, the apparent K permeability increases one order of magnitude as compared to the control condition before the ionic substitution. In Cl medium, the high levels of JinNa and of Jeff(K) observed in the steady state after (Na X K)i were interpreted as being a consequence of cell swelling. SCC and PD follow very different temporal patterns after (Na X K)i which are characterized by transients in SCC and a simple fall in PD. Reasons for these differences are discussed.

Evaluation of kinetic and energetic parameters of active sodium transport

Active sodium transport is classically analyzed in terms of an equivalent circuit, comprising an active conductance Ka and an electromotive force of sodium transport ENa. Although ENa is commonly considered the driving force of transport, model experiments have suggested that ENa is a composite parameter, incorporating both kinetic and energetic factors. An alternative approach considers both transport and the associated oxidative metabolism in terms of a nonequilibrium thermodynamic (NET) formulation, involving phenomenological coefficients and the affinity A, presumed to represent kinetic and energetic factors, respectively. Model experiments testing the NET formulation suggest that the affinity is indeed an energetic parameter. Calculated values of A in untreated frog skins and toad bladders range from about 20 to 80 kcal per mole of O2 consumption. Assuming a P/O ratio of 3, this range corresponds to about 3--13 kcal per mole of ATP utilization, values compatible with reported direct measurements. Although brief perturbations of transepithelial electrical potential deltapsi resulted in linear current-voltage relationship, indicating constancy of ENa and Ka, 15-min perturbations of deltapsi resulted in nonlinearity, indicating changes in ENa and Ka; perturbations of deltapsi enhancing active transport were associated with decrease of ENa and increase of Ka; slowing of active transport produced the converse effects.

Kinetics of bidirectional active sodium fluxes in the toad bladder

The kinetics of isotopic Na+ flows was studied in urinary bladders of toads from the Dominican Republic. Initial studies of the potential dependence of passive serosal to mucosal 22Na+ efflux demonstrated the absence of isotope interaction and/or other coupling with passive Na+ flow. The electrical current I and mucosal to serosal 22Na+ influx were then measured with transmembrane potential clamped at deltapsi=0, 25, 50, 75 or 100 mV. Subsequent elimination of active Na+ transport with mucosal amiloride permitted calculation of the rates of active Na+ transport JaNa and active and passive influx leads to JaNa and leads to JpNa. The results indicate that for Dominican toad bladders mounted in chambers only Na+ contributes significantly to transepithelial active ion transport; hence JaNa=Ja. Ja was abolished at deltapsi=E=96.3+/-1.9 (S.E.) mV. As deltapsi approached E, active efflux comes from Ja became demonstrable. At deltapsi=100 mV, comes from Ja exceeded leads to Ja, so that Ja was negative. Experimental values of leads to Ja agreed well with theoretical values predicted by a thermodynamic formulation: leads to Jaexp=0.985 leads to Jatheor (r=0.993). The dependence of leads to Ja on deltapsi is curvilinear.

Mechansims and components of renal tubular acidification

1. Renal cortical tubules of control and acetazolamide infused rats were perfused with 100 mM phosphate buffer at pH 5-5. The rate of alkalinization was measured by means of antimony micro-electrodes and was used to compute passive H ion fluxes from lumen to blood across the proximal and distal tubular epithelium. 2. The importance of other ionic movements that might contribute to pH changes of luminal buffers (chloride inflow into the lumen and bicarbonate diffusion across the epithelium) was assessed but found to be minor. H ion movements accounted for the majority of the observed pH changes. 3. H ion permeability of the tubular wall was calculated from the measured H fluxes and transepithelial concentration differences. It was 1-10 cm/sec, several orders of magnitude larger than those for other ions. However, such values are compatible with the mobility of protons in a medium of structure water within the limiting membrane. 4. A kinetic analysis of the mechanism of movement of H ions across the renal tubule is presented on the basis of experiments in which acidification and alkalinization of luminal buffers was followed in stationary microperfusions. The data are compatible with a pump-leak system in the proximal tubule, and with a model with low H ion permeability and a gradient dependent pump in the distal tubule.

Active sodium transport and the electrophysiology of rabbit colon

The electrophysiologic properties of rabbit colonic epithelial cells were investigated employing microelectrode techniques. Under open-circuit conditions, the transepithelial electrical potential difference (PD) averaged 20 mV, serosa positive, and the intracellular electrical potential (psimc) averaged -32 mV, cell interior negative with respect to the mucosal solution; under short-circuit conditions, psimc averaged -46 mV. The addition of amiloride to the mucosal solution abolishes the transepithelial PD and active Na transport, and psimc is hyperpolarized to an average value of -53 mV. These results indicate that Na entry into the mucosal cell is a conductive process which, normally, depolarized psimc. The data obtained were interpreted using a double-membrane equivalent electrical circuit model of the "active Na transport pathway" involving two voltage-independent electromotive forces (emf's) and two voltage-independent resistances arrayed in series. Our observations are consistent with the notions that: (a) The emf's and resistances across the mucosal and baso-lateral membranes are determined predominantly by the emf (64 mV) and resistance of the Na entry process and the emf (53 mV) and resistance of the process responsible for active Na extrusion across the baso-lateral membranes: that is, the electrophysiological properties of the cell appear to be determined solely by the properties and processes responsible for transcellular active Na transport. The emf of the Na entry process is consistent with the notion that the Na activity in the intracellular transport pool is approximately one-tenth that in the mucosal solution or about 14 mM. (b) In the presence of amiloride, the transcellular conductance is essentially abolished and the total tissue conductance is the result of ionic diffusion through paracellular pathways. (c) The negative intracellular potential (with respect to the mucosal solution) is due primarily to the presence of a low resistance paracellular "shunt" pathway which permits electrical coupling between the emf at the baso-lateral membrane and the potential difference across the mucosal membrane; in the absence of this shunt, the "well-type" electrical potential profile characteristic of rabbit colonic cells would be 'converted' into a "staircase-type" profile similar to those reported for frog skin and toad urinary bladder by some investigators.

Metabolic cost of sodium transport in toad urinary bladder

The metabolic cost of active sodium transport was determined in toad bladder at different gradients of transepithelial potential. Deltapsi, by continuous and simultaneous measurements of CO2 production and of transepithelial electric current. Amiloride was used to block active sodium transport in order to assess the nontransport-linked, basal, production of CO2 and the passive permeability of the tissue. From these determinations active sodium transport, Jna, and suprabasal CO2 production, Jsb CO2, were calculated. Since large transients in Jna and Jsb CO2 frequently accompanied any abrupt change in deltapsi, steady state conditions were carefully defined. Some 20 to 40 min were required after a change in deltapsi before steady state of transport activity and of CO2 production were achieved. The metabolic cost of sodium transport proved to be the same whether the bladder expended energy moving sodium against a transepithelial electrical potential grandient of +50 mV or whether sodium was being pulled through "the active transport pathway" by an electrical gradient of -50 mV. In both cases the value of the ratio Jna/Jsb CO2 averaged some 20 sodium ions transported per molecule of CO2 produced. When the Na pump was blocked by 10(-2) M ouabain, the perturbations of the transepithelial electrical potential did not elicit changes of Jna nor, consequently of Jsb CO2. The independence of the ratio Jna/Jsb CO2 from deltapsi over the range+/-50 mV indicates a high degree of coupling between active sodium transport and metabolism.

Thermodynamic analysis of active sodium transport and oxidative metabolism in toad urinary bladder

Measurements of electrical current and oxygen consumption were carried out concurrently under voltage clamp conditions in 11 toad hemibladders. Inhibition of active transport with amiloride then permitted evaluation of the passive conductance and the rate of basal oxygen consumption Jbr, allowing the simultaneous determination of the rates of active sodium transport JaNa and suprabasal oxygen consumption Jsbr-JaNa and Jabr were linear functions of the electrical potential difference over a range of +/- 80 mV. This allowed the comprehensive application of a linear nonequilibrium thermodynamic formalism, leading to the evaluation of the affinity A (negative free energy) of the metabolic reaction driving transport, all phenomenological coefficients, and the degree of coupling q relating transport to metabolism. Values of A determined by two techniques were A1=56.0 +/- 5.8 and A2=58.2 +/- 6.5 kcal per mole. Values of q determined by two techniques agreed well and were less than 1, indicating incompleteness of coupling, and hence lack of fixed stoichiometry between Na transort and O2 consumption. The affinity and the electromotive force of sodium transport ENa are not closely correlated, reflecting the fact that ENa comprises both kinetic and energetic factors.

Sodium transport and oxygen consumption in toad bladder. A thermodynamic approach

The relationship between active sodium transport and oxygen consumption was investigated in toad urinary bladder exposed to identical sodium-Ringer's solution at each surface, while controlling the transepithelial electrical potential difference delta phi. Rates of sodium transport and oxygen consumption were measured simultaneously, both in the short-circuited state (delta phi = 0) and when delta phi was varied. Under short-circuit conditions, when the rates of active sodium transport changed spontaneously or were depressed with amiloride, the ratio of active sodium transport to the estimated suprabasal oxygen consumption Na/O2 was constant for each tissue, but varied among different tissues. Only when delta phi was varied did the ratio Na+/O2 change with the rate of active sodium transport; under these circumstances dNa+/dO2 was constant but exceeded the ratio measured at short-circuit [(Na+/O2)delta phi = 0[. This suggests that coupling between transport and metabolism is incomplete. The results are analyzed according to the principles of nonequilibrium thermodynamics, and intepreted in terms of a simple model of the transepithelial sodium transport system.

The thermodynamic degree of coupling between metabolism and sodium transport in frog skin

The tightness of coupling between two processes is advantageously evaluated by the thermodynamic degree of coupling q, varying in absolute value from zero for uncoupled processes to unity for processes which are related stoichiometrically. Two methods for the determination of q in the active pathway in frog skin have been developed, employing amiloride to abolish active sodium transport. The values of q in 6 frog skins varied, but were always less than unity (mean 0.79 +/- 0.06 S.E. according to one method, 0.78 +/- 0.06 S.E. according to the other). This indicates that metabolism and sodium transport are incompletely coupled in this tissue even when passive transepithelial leakage pathways are taken into account.

Active H+ transport in the turtle urinary bladder. Coupling of transport to glucose oxidation

The turtle urinary bladder acidifies the contents of its lumen by actively transporting protons. H+ secretion by the isolated bladder was measured simultaneously with the rate of 14CO2 evolution from [14C]glucose. The application of an adverse pH gradient resulted in a decline in the rate of H+ secretion (JH) and in the rate of glucose oxidation (JCO2). The changes in JH and JCO2 were linear functions of the pH difference across the membrane. Hence, JH and JCO2 were linearly related to each other. The slope, deltaJH/deltaJCO2 was found to be similar in half-bladders from the same animal but was seen to vary widely in a population of turtles. To investigate the effect of pH gradients on deltaJH/deltaJCO2, two experiments were performed in each of 14 hemibladders. In one, JH and JCO2 were altered by changing the luminal pH. In the other, they were altered by changing the ambient pCO2 while the luminal pH was kept constant. The average slope, deltaJH/deltaJCO2, in the presence of pH gradients was 14.45 eq-mol-1. In the absence of gradients in the same hemibladders it was 14.72, delta = 0.27 +/- 1.46. The results show that H+ transport is organized in such a way that leaks to protons in parallel to the pump are negligible. Analysis of the transport system by use of the Essig-Caplan linear irreversible thermodynamic formalism shows that the system is tightly coupled. The degree of coupling, q, given by that analysis was measured and found to be at or very near the maximum theoretical value.

Effects of electrical gradients on volume flows across gall bladder epithelium

A volumetric method has been developed which permits continuous registration of volume flows across epithelial tissues. The method was applied to volume flow measurements across rabbit gall bladder epithelium. The rate of fluid reabsorption measured in this way was twice as high as previously observed in sac preparations of the gall bladder. This is probably due to better aeration and stirring of the mucosal solution. It was demonstrated that electrical gradients across the gall bladder induced volume flows towards the negative electrode. In non-transporting bladders volume flows were linearly related with current between 300 and 900 muA in both directions. However, volume flow rates were three times higher from mucosa to serosa than in the opposite direction. From the magnitude of polarization potentials, observed after switching off the current, the conclusion was reached that all of the current-induced volume flow is an osmotic flow due to salt polarization in the unstirred layers of the tissue. By implication, so-called streaming potentials observed during osmotic flows reflect solely polarization effects. In actively transporting gall bladders a 200 muA current increased or decreased the flow rate twice as much as expected from polarization effects alone. Therefore passage of current interfered directly with the active transport mechanism of gall bladder epithelium.

Effects of 2-deoxy-D-glucose, amiloride, vasopressin, and ouabain on active conductance and ENa in the toad bladder

The effects of various agents on active sodium transport were studied in the toad bladder in terms of the equivalent circuit comprising an active conductance Ka, an electromotive force ENa, and a parallel passive conductance Kp. For agents which affect Ka, but not ENa or Kp, the inverse slope of the plot of total conductance K against short-circuit current IO evaluates ENa, and the intercept represents Kp. Studies employing 5 X 10(-7) M amiloride to depress Ka indicate a changing ENa, invalidating the use of the slope technique with this agent. An alternative suitable technique employs 10(-5) M amiloride, which reduces IO reversibly to near zero without effect on Kp. Despite curvilinearity of the K-IO plot under these conditions, Kp may therefore be estimated fairly precisely from the residual conductance. It then becomes possible to follow the dynamic behavior of Ka and ENa (in the absence of 10(-5) M amiloride) by frequent measurements of K and IO, utilizing the relationships Ka=K-Kp, and ENa=IO/(K-Kp). 2-deoxy-D-glucose (7.5 X 10(-3)M) depressed both Ka and ENa. All of the above effects were noted promptly; Kp was unaffected. The "electromotive force of Na transport" ENa appears not to be a pure energetic parameter, but to relfect kinetic factors as well, in accordance with thermodynamic considerations.

A comparative study of the effects of norepinephrine and vasopressin on Na transport and O2 consumption in frog skin

Experiments were designed to compare the effects of two hormones-vasopressin and norepinephrine-on the energetics of Na transport in frog skin. Simultaneous measurements of O2 consumption and net Na flux were performed in the same skins by means of O2 cathodes and the short circuit current technique. The results showed that both hormones induced similar increments in Na transport. In contrast, there was a conspicuous difference in O2 consumption values, norepinephrine having a very small stimulatory effect compared to the one induced by vasopressin. Thus, despite the fact that both hormones increase Na permeability of frog skin by similar mechanisms and to a similar extent, they appear to exert very different effects on cell metabolism.

The electrical potential profile of gallbladder epithelium

In this study the relative ionic permeabilities of the cell membranes of Necturus gallbladder epithelium have been determined by means of simultaneous measurement of transmural and transmucosal membrane potential differences (PD) and by ionic substitution experiments with sodium, potassium and chloride ions. It is shown that the mucosal membrane is permeable to sodium and to potassium ions. The baso-lateral membrane PD is only sensitive to potassium ions. In both membranes chloride conductance is negligible or absent. The ratio of the resistances of the mucosal and baso-lateral membranes, RM/RS, increases upon reducing the sodium concentration in the mucosal solution. The same ratio decreases when sodium is replaced by potassium which implies a greater potassium than sodium conductance in the mucosal membrane. The relative permeability of the shunt for potassium, sodium and chloride ions is: PK/PNa/PCl=1.81:1.00:0.32. From the results obtained in this study a value for the PK/PNa ratio of the mucosal membrane could be evaluated. This ratio is 2.7. From the same data the magnitude of the electromotive forces generated across the cell membranes could be calculated. The EMF's are -15mV across the mucosal membrane and -81mV across the baso-lateral one. Due to the presence of the low resistance shunt the transmucosal membrane PD is -53.2mV (cell inside negative) and the transmural PD is +2.6mV (serosal side positive). The change in potential profile brought about by the low resistance shunt favors passive entry of Na ions into the cell across the mucosal membrane. Calculations show that this passive Na influx is maximally 64% of the net Na flux estimated from fluid transport measurements. The C-1 conductive of the baso-lateral membrane is too small to allow electrogenic coupling of C1 with Na transport across this membrane. Experiments with rabbit gallbladder epithelium indicate that the membrane properties in this tissue are qualitatively similar to those of Necturus gallbladder epithelium.

A comparison of the effects of ouabain and 2-deoxy-D-glucose on the thermodynamic variables of the frog skin

Previous studies support the validity of a linear thermodynamic formalism relating the rates of active Na-+ transport and oxygen consumption Jr to the electrical potential difference delta-psi and the affinity A (negative free energy) of the metabolic driving reaction. The formulation was further tested in paired control and experimental hemiskins by the use of two inhibitors of Na-+ transport. Ouabain, a specific inhibitor of the Na-+ pump, might be expected to diminish the dependence of Jr on delta-psi without affecting A, whereas 2-deoxy-D-glucose, a competitive inhibitor of glucose metabolism should be expected to diminish A. Both inhibitors were used at concentrations adequate to depress Na-+ transport (i.e. short-circuit current Io) to some 50% of control level. Measurements were made of Io and dJr/d(delat-psi), and the apparent value of the affinity Aapp was calculated according to the thermodynamic formulation. Ouabain depressed minus dJr/d(delta-psi) without affecting Aapp whereas 2-deoxy-D-glucose depressed Aapp without affecting minus dJr/d(delta-psi). The demonstration of these effects indicated the utility of the formalism.

Energetics of active transport processes

Active sodium transport across epithelial membranes has been analyzed by means of linear nonequilibirium thermodynamics. In this formulation the rates of active sodium transport JNa and the associated metabolic reaction Jr are postulated to be linear functions of both the electrochemical potential difference of sodium--XNa and the affinity A (negative free energy) of the metabolic reaction of driving transport. Experimental studies in various epithelia demonstrate that both JNa and Jr (oxygen consumption) are indeed linear functions of XNa. Theoretical considerations and experimental studies in other systems suggest that likelihood of linearity in A as well. If so, A may be evaluated. Several observations indicate that the quantity A evaluated from the thermodynamic formalism does in fact reflect the substrate-product ratio of the metabolic reaction which supports transport. This is in contrast to measurements of mean cellular concentrations, which may not reflect conditions at the site of transport. Associated studies of isotope kinetics permit the distinction between effects on the permeability of the active and passive transport pathways. With these combined approaches, it may prove possible to characterize both the energetic and permeability factors which regulate transport. The formulation has been applied to an analysis of the mechanism of action of the hormone aldosterone.

Nonequilibrium thermodynamic analysis of the coupling between active sodium transport and oxygen consumption

Sodium transport and oxygen consumption have been simultaneously studied in the short-circuited toad skin. A constant stoichiometric ratio was observed in each skin under control condition (NaCl-Ringer's solution bathing both sides of the skin) and after block of sodium transport by ouabain. During alterations of sodium transport by removal and addition of K to the internal solution the stoichiometric ratio is constant although having a value higher than that observed in other untreated skins. The coupling between active sodium transport and oxygen consumption was studied after a theoretical nonequilibrium thermodynamic model. Studies were made of the influence of Na chemical potential difference across the skin on the rates of Na transport and oxygen consumption. A linear relationship was observed between the rates of Na transport and oxygen consumption and the Na chemical potential difference. Assuming the Onsager relationship to be valid, the three phenomenological coefficients which describe the system were evaluated. Transient increases in the rate of sodium transport and oxygen consumption were observed after a transitory block of sodium transport by removal of Na from the external solution. Cyanide blocks completely the rate of oxygen consumption in less than 2 min and the short-circuit current measured after that time decays exponentially with time, suggesting a depletion of ATP from a single compartment.

Influence of transepithelial potential difference on the sodium uptake at the outer surface of the isolated frog skin

The unidirectional uptake of sodium across the outer surface of the isolated frog skin (J(12) (Na)) was measured in the presence of transepithelial potential difference (Delta(psi)) ranging from +100 to -100 mV. With a sodium concentration of 115 mM in the bathing solutions J(12) (Na) increases significantly when the spontaneous Delta(psi) is reduced to zero by short-circuiting the skin. With an Na concentration of 6 mM a progressive increase J(12) (Na) can be observed when Delta(psi) is decreased in several steps from +100 to -100 mV (serosal side positive and negative, respectively). The observed change J(12) (Na) amounts to a fraction only of that predicted from the shift in Delta(psi). The results suggest that under open circuit conditions the potential step across the outside surface is at most one half of Delta(psi) and that the resistance across the outside and inside barrier of the skin is ohmic. This is in agreement with measurements of intracellular potentials in the frog skin and with resistance measurements carried out in the toad skin. The data strongly support the view that the saturating component of J(psi) proceeds via a charged carrier system. Exposure to negative values of Delta(psi) of 50 mV or more for times of 24 min or more result in a marked reduction of J(12) (Na) which shows only partial or no reversibility.

Aldosterone action and sodium- and potassium-activated adenosine triphosphatase in toad bladder

Urinary hemibladders obtained from toads soaked in water or saline were treated with aldosterone, 10(-6) M, either 1(1/2) or 16 h after mounting. After 2(1/2) h exposure to the hormone, short-circuit current was increased by 110-192% and open-circuit potential by 20-44% as compared with untreated paired hemibladders. Mucosal cells were then assayed for sodium-potassium-stimulated adenosine triphosphatase (ATPase). No increase occurred in activity per milligram protein or in the portion of total activity dependent on sodium. Activity at low sodium concentrations was also measured and analyzed by means of the Hill equation in terms of K, the apparent dissociation constant of the enzyme-sodium complex, and n, a number that expresses the degree of interaction between binding sites. Neither K nor n was significantly altered by aldosterone. A few experiments were also carried out at low ATP concentrations (0.3 mM); again no change in sodium-dependent activity was noted. The results indicate that aldosterone does not stimulate sodium transport by increasing the quantity of sodium-potassium adenosine triphosphatase in mucosal cells or the dependence of this activity on sodium or ATP concentrations.