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

Cellular mechanisms of oxygen chemoreception in the carotid body

The carotid bodies (CB) are arterial chemoreceptors that by sensing changes of arterial PO2, PCO2 and pH can initiate and modify ventilatory and cardiovascular reflexes in order to maintain PO2, PCO2 and pH within physiological levels. It is now generally accepted that the glomus or type I cells of the CB are the transducers of hypoxic stimuli, and relay chemosensory information to the brainstem via neurotransmitter release at synaptic contacts with afferent terminals of the carotid sinus nerve. This article reviews the mechanisms of the O2-sensing process at the cellular level. We consider first the transduction of the hypoxic stimulus, in which most of the experimental evidence currently favors a mechanism involving modulation of the electrical properties of type I cells. The last part of the article deals with the transmission of the stimulus between type I cells and afferent nerve terminals, and we present an overview on the issue of neurotransmission in the CB, summarizing the actions of the main neurotransmitters present in the organ.

Oxygen uptake of isolated toad skin epithelium: micromeasurement and effect of ionic acclimation

Oxidative metabolism of isolated toad skin epithelium (Bufo viridis) was investigated in vitro under open-circuit conditions using the spectrophotometric oxyhemoglobin micromethod. This highly sensitive technique has been adapted for studying several epithelia in parallel and for detecting possible regional variations of oxygen uptake in individual epithelium. Changes in the proportion of mitochondria-rich cells (MRC) by ionic acclimation affected oxidative metabolism under nontransporting condition. After acclimation of animals to either NaNO3 or NaCl solutions (100 mmol/l, for greater than 2 wk), the number of MRC per square millimeter in epithelia from nonacclimated and NaNO3- and NaCl-acclimated animals was 350 +/- 113, 460 +/- 196, and 107 +/- 52, respectively. O2 uptake of nonacclimated and NaNO3-acclimated epithelia was significantly higher than that of NaCl-acclimated epithelia (i.e., 0.89 and 0.90 vs. 0.57 nmol O2.h-1.mm-2, respectively). The correlation established between O2 uptake and number of MRC allowed evaluation of the respiration rate of one single MRC, i.e., approximately 1 pmol O2/h. The lowest mitochondrial oxidative activity was found in the epithelia from NaCl-acclimated toads where the uncoupler 2,4-dinitrophenol (50 mumols/l) had the highest relative stimulatory effect (+114%). Acetazolamide (50 mumols/l), a potent inhibitor of carbonic anhydrase mainly present in the MRC, reduced selectively by 31% O2 uptake of the MRC-rich epithelia (NaNO3 acclimated). O2 uptake increased significantly by approximately 80% when basolateral pH increased from 5.8 to 7.8, but did not depend on apical pH. These findings indicate that under nontransporting (open-circuit) conditions, aerobic metabolism of the isolated toad skin epithelium is related to the density and/or characteristics of the MRC.(ABSTRACT TRUNCATED AT 250 WORDS)

pH-stat experiments in proximal renal tubules

The pH-stat technique has been used to measure H+ fluxes in gastric mucosa and urinary bladder "in vitro" while keeping mucosal pH constant. We now report application of this method in renal tubules. We perfused proximal tubules with double-barreled micropipettes, blocked luminal fluid columns with oil and used a double-barreled Sb/reference microelectrode to measure pH, and Sb or 1 N HC1-filled microelectrodes to inject OH- or H+ ions into the tubule lumen. By varying current injection, pH was kept constant at adjustable levels by an electronic clamping circuit. We could thus obtain ratios of current (nA) to pH change (apparent H(+)-ion conductance). These ratios were reduced after luminal 10(-4) M acetazolamide, during injection of OH-, but they increased during injection of H+. The point-like injection source causes pH to fall off with distance from the injecting electrode tip even in oil-blocked segments. Therefore, a method analogous to cable analysis was used to obtain H+ fluxes per cm2 epithelium. The relation between JH+ and pH gradient showed saturation kinetics of H fluxes, both during OH- and H+ injection. This kinetic behavior is compatible with inhibition of JH by luminal H+. It is also compatible with dependence on Na+ and H+ gradients of a saturable Na/H exchanger. H(+)-ion back-flux into the tubule lumen also showed saturation kinetics. This suggests that H+ flow is mediated by a membrane component, most likely the Na(+)-H+ exchanger.

Oxygen consumption and active sodium and chloride transport in bovine tracheal epithelium

The O2 consumption (Jr) and the short-circuit current (Ji) were measured simultaneously in bovine tracheal epithelium in vitro. In this tissue, Ji is the sum of two active transport processes, Cl- secretion and Na+ absorption. Jr was determined from the decrease of PO2 in the incubation solution, at 37 +/- 0.05 degrees C and at a PO2 around 600 torr. Microbial contamination and leaks of dissolved O2 from the solution never exceeded 4% of the rate of PO2 decrease due to the O2 consumption of the tissue. Ji and Jr were stable over 5 h of incubation under standard conditions. Ji was 106 +/- 4 nequiv min-1 cm-2 and Jr was 39.8 +/- 1.1 nmol O2 min-1 cm-2 (mean +/- S.E., n = 46). Ji was varied with several agents known to affect ion transport across the tracheal epithelium. Na+ absorption was inhibited partly with amiloride or completely following Na+ substitution with choline. Cl- secretion was selectively suppressed by furosemide. Ji was also reduced to a very low level, using ouabain or K+ suppression to inhibit the Na+-K+-ATPase. All these manoeuvres resulted in significant reductions of both Ji and Jr. Basal Jr was not affected when Ji was modified. A plot of the relative change in suprabasal Jr versus the relative change of Ji gave a straight line (r = 0.98, n = 60). A plot using absolute values yielded a stoichiometric ratio of 13.9 ions per O2 molecule, for Na+ as well as for Cl-. The stoichiometric ratio was also calculated for each experiment. Its mean value was 14.9 ions per O2 molecule. The population of the ratios was widely dispersed, but this was explained as a predictable statistical phenomenon.

Active transport: conditions for linearity and symmetry far from equilibrium

The impressive linearity of force-flow relationships in epithelial active-transport systems suggests the utility of a linear, nonequilibrium-thermodynamic analysis. We here present a plausibility argument for the appropriateness of such a treatment. Conventional phenomenological equations of nonequilibrium thermodynamics constitute an incomplete description of the processes under study, because a given thermodynamic force may be induced in an infinite number of ways. In general, therefore, flows are nonlinear functions of the forces, and the Onsager reciprocal relations are obeyed only very near equilibrium. If, however, the forces of two coupled processes can be constrained to "proper" pathways, each flow is a linear function of each force, and the phenomenological cross-coefficients are equal far from equilibrium. The nature of such proper pathways is investigated in terms of a simple model of a sodium-active transport system. Where the treatment is appropriate (i.e., for sufficiently small perturbations about a steady state far from equilibrium) it permits a complete thermodynamic characterization of a system, even when only one of the two forces can be controlled experimentally while the other remains constant.

Nonequilibrium linear behavior of biological systems. Existence of enzyme-mediated multidimensional inflection points

The linear phenomenological equations of nonequilibrium thermodynamics are limited theoretically to near equilibrium although a number of biological systems have been shown to exhibit a "linear" relationship between steady-state flows and conjugate thermodynamic forces outside the range of equilibrium. We have found a multidimensional inflection point which can exist well outside the range of equilibrium around with enzyme-catalyzed reactions exhibit "linear" behavior between the logarithm of reactant concentrations and enzyme catalyzed flows. A set of sufficient conditions has been derived which can be applied to any enzyme mechanism to determine whether a multidimensional inflection point exists. The conditions do not appear overly restrictive and may be satisfied by a large variety of coupled enzyme reactions. It is thus possible that the linearity observed in some biological systems may be explained in terms of enzyme operating near this multidimensional point.

Transient potassium fluxes in toad skin

Experiments were carried out in the isolated short-circuited skin of the toad Bufo marinus ictericus. 42K influx and efflux experiments were carried out with skins bathed on both sides by NaCl-Ringer's solution. Those fluxes showed very similar kinetics of equilibration with time and the results could be fitted by equations of a model of two intraepithelial compartments and the bathing solutions. In the steady state K influx is 3.99 +/- 0.36 nmol cm-2 hr-1 (n = 7) and efflux 3.62 +/- 0.38 nmol cm-2 hr-1 (n = 7) and are not statistically different, indicating that no net K flux is present across the epithelium. Different kinds of perturbations affecting the rates of 42K discharge into the bathing solutions were studied. Immediately after addition of amiloride (10(-4) M) to the outer solution, a sharp decline is observed in the rate of 42K discharge into the bathing solution, JK21, which falls from 3.62 +/- 0.38 nmol cm-2 hr-1 to 2.02 +/- 0.04 nmol cm-2 hr-1 (n = 7) 2 min after addition of the drug, followed by a partial recuperation with time. A complete Na by K substitution in the outer bathing solution induces a prompt and marked decline in JK21 which is similar to that induced by amiloride. Increase in the outer bathing solution Na concentration from zero Na concentration induces a nonlinear increase in JK21 and a linear relationship was observed between JK21 and short-circuit current in the range of 0 to 115 mM external Na concentration. The decline in JK21 induced by amiloride or by lowering external Na concentration was interpreted as being caused by electrical hyperpolarization of the external barrier of the epithelium induced by these procedures. Depolarization of the epithelial barriers by inner Na by K substitution in the short-circuited state (when the potential barriers are equal) drastically interfere with the rate of 42K discharge from the epithelium into the bathing solutions. Thus, transient increases are observed both in the rate of 42K discharge to the outer and to the inner bathing solutions upon depolarization of the barriers. These results indicate that at least the most important component of transepithelial K unidirectional fluxes goes through a transcellular route with a negligible paracellular component. Addition of ouabain (10(-3) M) to the inner bathing solution induces a transient rise in the rate of 42K discharge to the outer bathing solution with a peak on the order of 200% of the stationary value previous to the action of the inhibitor, followed by a return to new stationary values not statistically different from those observed previously to the effect of ouabain. The behavior of JK21 upon the effect of ouabain, as suggested by comparison with predictions from computer simulation, strongly supports the notion of a rheogenic Na pump in the inner barrier of the epithelium against the notion of a nonrheogenic 1:1 Na--K pump.

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.

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.

Oxygen consumption by frog skin and its isolated epithelial layers as a function of their sodium-transporting activity

The metabolic cost (in terms of oxygen consumption) of transcellular sodium transport was assessed on ventral frog skin and its isolated epithelial layers, by measuring the decrease in oxygen consumption by the tissue upon transient withdrawal of sodium from the outside solution. The same number of sodium ions was transported per molecule oxygen consumed whole skin (17.4 +/- 2.3) and its isolated epithelium (17.3 +/- 2.4). The metabolic cost of sodium transport could not be estimated properly when this process was blocked by amiloride or ouabain, as these drugs were found to bring about an increase in oxygen consumpton by the tissue when no sodium was available for transport.

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.

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.

H in cortical peritubular capillaries of rat kidney

The pH of peritubular capillaries was measured by means of antimony microelectrodes, during their perfusion with mammalian Ringer's solutions at different pH, in control and acetazolamide infused rats. In capillaries perfused with a solution more acid than blood, significant alkalinization was observed at increasing distances from the point of perfusion, while during perfusions with more alkaline solutions, acidification was observed. Plotting the pH change observed per micrometer of distance from the perfusion point against the pH of the perfusing solution, the pH in equilibrium with tubular cells was interpolated. A value of 7.51 +/- 0.01 was found for control rats, significantly higher than the mean arterial blood pH of this group, of 7.39. In acetazolamide infused rats an equilibrium pH of 7.44 +/- 0.02 was found, still higher than the blood pH of 7.34. The slope of these lines was significantly greater in control than in acetazolamide treated rats. This slope was shown to evaluate permeability to the ions responsible for acid-base balance. The present data suggest that peritubular alkalinization is reduced after carbonic anhydrase inhibition due to decreased peritubular permeability to the involved ions, which represents a further site of action of these inhibitors.

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.

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.