Alvin Essig

Energetics of Active Transport Processes

Discussions of active transport usually assume stoichiometry between the rate of transport J(+) and the metabolic rate J(r). However, the observation of a linear relationship between J(+) and J(r) does not imply a stoichiometric relationship, i.e., complete coupling. Since coupling may possibly be incomplete, we examine systems of an arbitrary degree of coupling q, regarding stoichiometry as a limiting case. We consider a sodium pump, with J(+) and J(r) linear functions of the electrochemical potential difference, -X(+), and the chemical affinity of the metabolic driving reaction, A. The affinity is well defined even for various complex reaction pathways. Incorporation of a series barrier and a parallel leak does not affect the linearity of the composite observable system. The affinity of some region of the metabolic chain may be maintained constant, either by large pools of reactants or by regulation. If so, this affinity can be evaluated by two independent methods. Sodium transport is conveniently characterized by the open-circuit potential (Deltapsi)(I=0) and the natural limits, level flow (J(+))(X+=0), and static head X(0) (+) = (X(+))(J+=0). With high degrees of coupling -X(0) (+)/F approaches the electromotive force E(Na) (Ussing); -X(0) (+)/F cannot be identified with ((RT/F) ln f)(X+=0), where f is the flux ratio. The efficiency eta = -J(+)X(+)/J(r)A is of significance only when appreciable energy is being converted from one form to another. When either J(+) or -X(+) is small eta is low; the significant parameters are then the efficacies epsilon(J+) = J(+)/J(r)A and epsilon(X+) = -X(+)/J(r)A, respectively maximal at level flow and static head. Leak increases both J(+) and epsilon(J+) for isotonic saline reabsorption, but diminishes -X(0) (+) and epsilon(Xfemale symbol). Electrical resistance reflects both passive parameters and metabolism. Various fundamental relations are preserved despite coupling of passive ion and water flows.

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

SummaryThe effects of various agents on active sodium transport were studied in the toad bladder in terms of the equivalent circuit comprising an active conductanceKa, an electromotive forceENa, and a parallel passive conductanceKp. For agents which affectKa, but notENa orKp, the inverse slope of the plot of total conductance κ against short-circuit currentI0 evaluatesENa, and the intercept representsKp. Studies employing 5×10−7m amiloride to depressKa indicate a changingENa, invalidating the use of the slope technique with this agent. An alternative suitable technique employs 10−5m amiloride, which reducesI0 reversibly to near zero without effect onKp. Despite curvilinearity of the κ-I0 plot under these conditions,Kp may therefore be estimated fairly precisely from the residual conductance. It then becomes possible to follow the dynamic behavior ofKa andENa (in the absence of 10−5m amiloride) by frequent measurements of κ andI0, utilizing the relationshipsKa=K-Kp, andKNa=IO/(K-Kp). 2-deoxy-d-glucose (7.5×10−3m) depressedKa without affectingENa. Amiloride (5×10−7m) depressedKa and enhancedENa. Vasopressin (100 mU/ml) enhancedKa markedly and depressedENa slightly. Ouabain (10−4m) depressed bothKa andENa. 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 reflect kinetic factors as well, in accordance with thermodynamic considerations.

Energetics of Active Transport

In discussing questions of active transport from the viewpoint of linear nonequilibrium thermodynamics it is in a sense superfluous to acknowledge the influence of Aharon Katchalsky. Suffice it to say that this work, which was carried out in close collaboration with Roy Caplan, was begun when we were both working in Ora Kedems laboratory in Aharons Polymer Department at the Weizmann Institute of Science. Our debt will be evident throughout. The energetics of active transport is commonly discussed in terms of active sodium transport. There are two reasons for this. For one, sodium transport is very widespread in animal tissues—in some opinions, ubiquitous. Second, very convenient experimental systems are available for the study of this process. Thanks to the work of Ussing with frog skins (Ussing and Zerahn, 1951; Ussing, 1960), and later Leaf with toad bladder (Leaf et al., 1958), we have available two fairly simple epithelial membranes that can be used as experimental model systems. When either of these membranes is mounted in an experimental apparatus of the sort shown in Fig. 1, and exposed to physiological saline solutions at each surface, an electrical potential difference is generated. This is the consequence of active sodium transport from the outer surface of the frog skin (or the urinary surface of the toad bladder) across the tissue into the body fluid. In appropriate species, essentially only sodium is transported actively. Consequently it is possible to manipulate the electrical potential by the use of appropriate circuitry, and to measure the rate of active sodium transport instantaneously and continuously with a microammeter. Thus the effect of experimental manipulations, for example the addition of drugs or hormones, can be observed immediately. It is easy to understand why so convenient an experimental apparatus has been widely used in study of the energetics of active transport. Unfortunately, however, it seems to us that the classical approach to this subject has suffered from fundamental conceptual shortcomings. First, studies of the energetics of active sodium transport have often laid considerable em-

The effect of aldosterone on the energetics of sodium transport in the frog skin

Abstract Uncertainty persists as to whether the stimulation of active sodium transport by aldosterone is attributable to effects on permeability or energetic factors. This question has been examined with the aid of a thermodynamic formulation in which the rate of both active sodium transport JNa and O2 consumption Jr are assumed to be linear functions of the electrical potential difference Δψ and the affinity A (negative free energy) of metabolic reaction. Previous studies have indicated constancy of a characteristic affinity on perturbation of Δψ, suggesting the possibility of its evaluation. In studies of paired frog skins the admnistration of aldosterone led to a significant increase in the short-circuit current I0, a suggestive increase in the associated rate of O2 consumption Jro, and a significant increase in the ratio −I 0 { d J r / d (Δψ)} dJ r d(δψ) . If linearity obtains this ratio is equal to A. Depression of active sodium transport and the associated metabolism with amiloride, which depresses permeability, also results in an increase in the apparent affinity −I 0 { d J r / d (Δψ)} dJ r d(δψ) . The results indicate that aldosterone does not act simply by increasing the permeability or the number of transport units operating in parallel, but suggests that energetic factors are implicated as well.

Contribution of junctional conductance to the cellular voltage-divider ratio in frog skins

It has been suggested that distribution of lateral interspace resistance in association with a highly conductive junction can significantly affect the measurement of outer membrane(o)/epithelial(t) voltage divider ratios (Fo=δVo/δVt), thereby leading to erroneous inferences regarding the outer membrane fractional resistance [fRo=Ro/Rc=Ro/(Ro+Ri)], whereRo andRi are the outer and inner cell membrane resistance respectively andRc is the total cell membrane resistance. We present here experimental evidence for this point of view. During seasons when frog skins were highly permeable to Cl, transepithelial conductancegt often exceeded 2 mS/cm2. High concentrations of external amiloride rapidly blocked cellular transport, butgt initially remained high andFo remained appreciably less than 1.0. These values ofFo were found here to result from low junctional resistanceRj: increase ofRj, either gradually following the administration of amiloride, or abruptly with external replacement of Cl by other anions, was associated with increase ofFo to near unity, without effect on the membrane potential or significant change in the short-circuit current. Experimental results following amiloride validated a simple equivalent circuit model predicting near-linear increase inFo with progressive decrease ingt and led to plausible values ofRj and lateral space resistanceRl. The possible influence of the paracellular resistance pattern on the evaluation of cell membrane resistances from voltage divider ratios is discussed.

Effect of aldosterone on active and passive conductance and ENA in the toad bladder.

SummaryIt has been demonstrated previously that aldosterone increases the electrical conductance of the toad bladder in association with the stimulation of active sodium transport. In the present study the concurrent measurement of electrical quantities and ion tracer flux distinguishes effects on active and passive pathways. Lack of an effect on passive Na+ or Cl− tracer flux in hemibladders preselected to eliminate large artefactual leaks indicates that aldosterone has no influence on physiological passive conductance. Thus, the enhancement of electrical conductance is entirely attributable to the active pathway. The magnitude of the increase in the active conductance was estimated. The data permitted also the comparison of effects on the flux ratio of Na+ at short circuit (f0) and the electrical potential difference adequate to abolish active sodium transport (ENa). Even in membranes with minimal leakage the flux ratio does not reliably reflectENa. Aldosterone increased meanf0 from 11 to 22, but did not affectENa.

Voltage-dependent K conductance at the apical membrane of Necturus gallbladder

The epithelial and cellular effects of clamping the transepithelial potential (Vt, mucosa reference) have been investigated in the Necturus gallbladder. Following initial equilibration at short circuit, tissue conductance gt was 4.1 +/- 1.2 (SD) mS/cm2, the apical potential Va was -76 +/- 8 mV, and the apical fractional voltage on brief voltage perturbation (fa = delta Va/delta Vt, reflecting the ratio of apical membrane to transcellular resistance) was 0.72 +/- 0.11 (21 gallbladders, 34 impalements). On clamping Vt at positive values, Va depolarized and fa decreased; at the same time gt decreased. Clamping Vt at negative values produced converse effects. All of the above changes were related directly to the magnitude of the clamping potential Vt and were reversed on return to the short circuit state. Effects of Vt on fa are not due to changes in the extracellular pathway resistances (which, however, contribute to gt). Furthermore, the effects of Vt on fa were abolished by the mucosal application of TEA or Ba, or acidification of the mucosal solution. Thus, these experiments disclose the presence of a voltage-dependent apical K conductance that increases with apical membrane depolarization. The calculated dose-response curve of TEA inhibition of apical conductance and the values of the apparent dissociation constant were in good agreement with those found for K channels in excitable tissues. Mucosal application of the Ca ionophore A23187 shifted the voltage dependence curve of fa to more negative values of Va without altering its shape. The effect of A23187 suggests a possible role of intracellular Ca in the modulation of the apical K channels.

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

SummaryMeasurements 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 consumptionJrb, allowing the simultaneous determination of the rates of active sodium transportJNaa and suprabasal, oxygen consumptionJrsb.JNaa andJrsb 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 affinityA (negative free energy) of the metabolic reaction driving transport, all phenomenological coefficients, and the degree of couplingq relating transport to metabolism. Values ofA determined by two techniques wereA1=56.0±5.8 andA2=58.2±6.5 kcal per mole. Values ofq determined by two techniques agreed well and were less than 1, indicating incompleteness of coupling, and hence lack of fixed stoichiometry between Na transport and O2 consumption. The affinity and the electromotive force of sodium transportENa are not closely correlated, reflecting the fact thatENa comprises both kinetic and energetic factors.

Voltage-dependence of Ca2+ uptake and ATP hydrolysis of reconstituted Ca2+-ATPase vesicles.

Ca2+-ATPase from sarcoplasmic reticulum was reconstituted into phospholipid/cholesterol (9:1) vesicles (RO). Sucrose density gradient centrifugation of the RO vesicles separated a light layer (RL) with a high lipid/protein ratio and a heavy layer (RH). RH vesicles exhibited a high rate of Ca2+-dependent ATP hydrolysis but did not accumulate Ca2+. RL vesicles, on the other hand, showed an initial molar ratio of Ca2+ uptake to ATP hydrolysis of approximately 1.0. Internal trapping of transported Ca2+ facilitated studies over periods of several minutes. Ca2+ transport and ATP hydrolysis declined concomitantly, reaching levels near 0 with external Ca2+ concentrations less than or equal to 2 microM. Ca2+ uptake was inhibited by the Ca2+ ionophore A23187, the detergent Triton X-100, and the metabolic inhibitor quercetin. Ca2+ transport generated a transient electrical potential difference, inside positive. This finding is consistent with the hypothesis that the Ca2+ pump is electrogenic. Steady state electrical potentials across the membrane were clamped by using potassium gradients and valinomycin, and monitored with voltage-sensitive dyes. Over a range of +50 to -100 mV, there was an inverse relationship between the initial rate of Ca2+ uptake and voltage, but the rate of ATP hydrolysis was nearly constant. In contrast, lowering the external Ca2+ concentration depressed both transport and ATP hydrolysis. These findings suggest that the membrane voltage influences the coupling between Ca2+ transport and ATP hydrolysis.

Kinetics of tracer flows and isotope interaction in an ion exchange membrane

SummaryThe thermodynamic formulation of isotope interaction (coupling of abundant and tracer isotope flows) has been tested in a highly permselective anion exchange membrane in the absence of significant electroosmosis. A previous study of Cl− permeation has now been extended to include permeation of I−, Acetate, and SO42− in different bath concentrations, with the use of both electrical and chemical driving forces. The flux ratios were “abnormal” according to the usual criteria for simple passive flow, but were closely predicted by the theoretical expression incorporating the influence of isotope interaction. In the absence of coupled flows of other chemical species the extent of isotope interaction can be determined either from the flux ratio or from the measurement of a single unidirectional flux at two settings of the electrochemical potential difference. Direct evidence of negative isotope interaction was presented.