Medical
Hypotheses
5:
247-252,
1979
LIMITATION OF RESISTANCE AS A PARAMETER BY WHICH TO CHARACTERIZE EPITHELIA THAT ACTIVELY TRANSPORT
IONS
Thomas W. Ziegler, Division of Nephrology, Veterans Administration Hospital, San Diego, California 92161 USA and University of California San Diego ABSTRACT It is theoretically inappropriate to characterize an actively transporting epithelium by "resistance" alone which is correctly applied only to passive circuit elements. Rather, such epithelia (if they actively transport sodium) require, as a minimum, characterization by an active circuit element parameter such as voltage (ENa), current (INa) or power (WNa) in some configuration with resistances. Recent experimental studies of epithelia which actively transport sodium have omitted consideration of the active circuit element and attributed all measured changes observed to "resistance" changes in the epithelium as the transepithelial sodium gradient is altered. It is suggested that the observed changes in voltage/current ratio could be consequences of changes in the electrical behavior of the active circuit element of such epithelia. It may be biologically impossible to suppress all electromotive forces in epithelia to measure the truly passive characteristics of the epithelium without destroying tissue viability. The actual methods used to date for measurement of "resistance" in epithelia consist of perturbing signals which might alter the electrical behavior of an active element such as an "ion pump"; the observed changes in voltage to current ratio observed in such experiments can be better explained by a change in the active ion pump rather than by changes in passive epithelial "resistance". Key Words:
epithelial transport, electrophysiology, toad bladder, frog skin, kidney tubule
membrane transport,
DEFINITION Resistance is a parameter used to characterize the physical properties of a conductor. An ohm (the unit of electric resistance) is the electric resistance between two points of a conductor when a constant difference of potential of 1 volt, applied between these two points, produces in this conductor a current of 1 ampere, this conductor not being the source of a 7 electromotive force (1). A conductor is a body incapable ofsupporting electic strain; a charge given to a conductor spreads to all parts of the body (2).
APPLICATION TO EPITHELIAL PHYSIOLOGY Measurements of "membrane resistance" in epithelial physiology ignore both of these definitions:(a) the membrane under study is usually the source of an electromotive force, viz. an ion 'pump" linked to exergonic metabolic reactions within the cell; and (b) biological membranes do continuously support an electric strain manifest as a persisting transmembrane potential Thus, biological membranes which, by virtue of exergonic metaboldifference. ic processes, generate and maintain transmembrane potential differences are not passive circuit elements, rather they are active circuit elements capable of injecting electrical energy into a circuit.
In epithelia which actively transport ions the major flow of ions is polarized in direction to produce the phenomena of secretion or absorption. In selected epithelia (those of the "tight" or non-leaky variety) all or almost all of the ion transport may occur through an electrogenic pathway. Specifically, this is known to occur in the frog skin (3) and toad bladder(4) where the net transepithelial sodium flux equals the short-circuit current. In such tissues, metabolically-linked active ion transport dominates the electrophysiological character of the epithelium. Thus by analogy to circuit theory, the tight epithelium behaves as a battery. Such an active circuit element is characterized by the potential it generates, ENa. A battery or P tight epithelium does possess an "internal resistance" a measure of the frictional loss on movement of electrons through the battery or ions through the epithelium. This loss is dissipated as heat. This "internal resistance" is a secondary or less important characteristic of the battery or tight epithelium and it does not govern the electrical behavior at the battery terminals or at the faces of the epithelium. Rather, for a battery, the E/I ratio observed at its terminals is not a characteristic of the battery itself, but rather is the negative of the resistance of the load applied to the battery. Under open-circuit conditions the battery possesses a characteristic potential E, no current is flowing, so 1=0, and the "resistance" of the battery is E/I = infinity. When the terminals of a battery are short-circuited by a wire of nil resistance, an infinite current would flow, and E/I, theoretically, would equal zero. Practical states of operation of the battery lie somewhere between these two cases and the E/I value for the battery will be the negative of the resistance of the applied load. This number is negative because the current flows through the battery in a direction opposite to the polarity of the battery's voltage. The analogous "load" applied to an actively sodium ion pumping epithelium is the sodium gradient against which the epithelium must deliver ions. Thus, an epithelium pumping sodium ions up a large sodium gradient would appear to have a large amplitude "resistance" or E/I ratio whereas an epithelium delivering sodium ions against a favorable sodium gradient would appear to have a lower amplitude "resistance" or E/I ratio. The value of E/I for the actively transporting epithelium is not a characteristic of the epithelium, but rather of the applied sodium gradient, or load. This explanation may be applied to the studies in toad urinary bladder which showed an increase in "tissue resistance" as mucosal sodium concentration was decreased and a decrease in "tissue resistance" as mucosal sodium concentration was increased (5) and correspondingly converse changes in "tissue resistance" as serosal sodium concentration was altered(6). Similar measurements of transepithelial "resistance" changes have been made 248
in the distal tubule of rat nephron (7). Again, "tissue resistance" decreased as the transepithelial sodium gradient was made more favorable and "tissue resistance" increased as the sodium gradient was made less favorable for transport of sodium. The epithelial "resistance" changes observed were attributed to changes in shunt "resistance", i.e. to structural changes in the epithelium which altered ion flow.
I would suggest that the changes in E/I ratio measured in toad bladder and distal tubule need not be consequences of resistance changes in cell membranes or paracellular pathways but could be better explained as changes in the active circuit element characteristics of the tight epithelia. The E/I value for the actively transporting epithelium is simply the negative of the applied load (sodium gradient). In electrophysiology it is difficult to satisfy the requirement that the conductor under consideration not be the source of any electromotive force. Ion transport processes are integral to cellular integrity and viability and methods which block active transport, such as metabolic inhibitors, may result in artifactual changes in cell membrane resistances. An attempt has been made to study the passive transport characteristics of epithelia after inhibition of the active sodium transport system with ouabain (8,9) but extensive electrophysiological studies have not yet been carried out under these conditions. Although it has not been definitively proven, there is reason to question whether ouabain completely inhibits active transport of sodium in frog skin as sodium does not distribute in accord with the Nernst equation after ouabain (10). Despite extensive theoretical analysis of active vs passive pathways of ion transport (e.g. refs. 11 and 12) most experimental studies of epithelial electrophysiology contain the tacit assumption that the electromotive force of the active transport system remains constant throughout the experimental maneuvers and that measured changes in the E/I ratio are due to passive or resistive changes (5-7, 18). Measurements
of "tissue resistance", though vigorously pursued in the faif to shed light on whether aldosterone stimulates transepithelial sodium transport by decreasing apical membrane resistance, by stimulating the basolateral active pump, by increasing energy delivery to the pump, by a combination of these, or by some other mechanism (13-17). Carefully conducted studies of agents known to modulate sodium transport in epithelia show that measurements of tissue conductance (gN ) (the reciprocal of resistance) do not clarify the site or mode of action o? 2-deoxy-D-glucose, amiloride, vasopressin, or ouabain (18). The latter study concludes that the conductance of the active pathway may dynamically interact with the force of the sodium pump in some fashion, thus gNa and ENa might not be independent variables. Thus, experiments designed to differentiate the locus of action of a drug or hormone on sodium transport as lying at the apical (resistive, passive) barrier for sodium entry or at the basolateral (active) pump step might well be destined to failure.
experimental
Jaboratory,
In analyzing the data from epithelial electrophysiology experiments in the future, I would suggest that actively transporting epithelia be characterized by parameters used to characterize active sources, namely voltage (ENa) or current (INa) in some combination With resistances. Although there is not 249
yet adequate or compelling evidence to require it, I would suggest that biological ion pumps in epithelia may be "work-limited" and that a characteristic "wattage" (WNa) might be the best electrophysiological parameter by which to characterize epithelia. The work accomplished by such transporting epithelia is the sum of the chemical work and the electrical work expended in ion transport. Thus as an epithelium pumps sodium ions against a large, unfavorable sodium gradient it will deliver only a small current, the same epithelium pumping sodium against a smaller, more favorable gradient could deliver a larger current. A "work-limited" ion pump provides a conceptual framework for interrelationship of INa and ENa, and hence provides a possible explanation for gNa and ENa not being independent variables. Interpretation of actual experimental data is facilitated by the assumption of a specific model for epithelial transport. I have suggested a model whereby the "resistive" character of the apical cell membrane and the "active pump character" of the lateral cell membrane are tightly coupled (19). Specifically, this is accomplished by a cytoplasmic sodium "transport pool" of almost infinitesimal size. Experimental demonstration of the electrophysiological character of an ion pump lying in the lateral cell wall of an epithelium will require methods for study which are not yet available. Specifically, it would be necessary to measure sodium activity and potential difference simultaneously in both cellular cytoplasm and adjacent lateral intercellular space fluid as well as ion flux through the pump. Measurement of epithelial resistance has been accomplished in numerous ways, but the method usually consists of application of a perturbing current pulse to the epithelium with measurement of the resulting voltage deflection. It is always tacitly assumed that the amplitude of the perturbing current does not alter the amount of current flowing through the active element of the epithelial cell system being measured (e.g. the "ion pump"). The microelectrode study of Reuss and Finn in the toad bladder (20) shows that the alteration in PD across the basolateral cell membrane follows the alteration in PD across the apical cell membrane within 15 milliseconds when the mucosal sodium entry is perturbed by increment of sodium or addition of amiloride. If the correct explanation for this phenomenon is an infinitesimally small then all measurements of epithelial cytoplasmic sodium "transport pool" (19), resistance made to date use pulses of current of such an amplitude and duration that they could grossly alter sodium activity in this cytoplasmic "transport pool" and thereby alter the electrical behavior of the active "ion pump". CONCLUSIONS (a) It is inappropriate to characterize an actively transporting epithelium by "resistance" alone which is correctly applied only to passive circuit elements; rather it is necessary to include consideration of the active component of ion transport in the analysis of epithelial electro(b) It may be biologically impossible to supphysiological experiments. press all electromotive forces in epithelia to measure the truly passive characteristics of the epithelium without losing the viability and integrity of the tissue; active transport of ions is a sine qua non for cellular viability. (c) Th e actual methods used to measure "rastance" that have been used to date consist of perturbing signals which might alter the 250
electrical behavior of the active ion pump in epithelia rather than serving as a "probe" of the passive, resistive components of the epithelia. REFERENCES 1.
Weast RC, editor. Handbook of Chemistry and Physics, 55th edition, CRC Press, Cleveland, Ohio, 1974-1975, p. F-119.
2.
ibid., p. F-88.
3.
Ussing HH, Zerahn K. Active transport of sodium as the source of electric current in the short-circuited isolated frog skin. Acta Physiol Stand 23: 110-127, 1951.
4.
Frazier HS, Leaf A. The electrical characteristics of active sodium transport in the toad bladder, J Gen Physiol 46: 491-503, 1963.
5.
Reuss L, Finn AL. Effects of changes in the composition of the mucosal solution on the electrical properties of the toad urinary bladder epithelium. J Membr Biol 20: 191-204, 1975.
6.
Finn AL, Reuss L. Effects of changes in the composition of the serosal solution on the electrical properties of the toad urinary bladder epithelium. 3 Physiol (Lond) 250: 541-558, 1975.
7.
OeBermudez L, Windhager EE. Osmotically induced changes in electrical resistance of distal tubules of rat kidney. Amer J Physiol 229: 1536-1546, 1975.
8.
Walser M, Hammond V, Butler S. Depolarization increases susceptibility of toad bladder sodium transport to inhibition by ouabain. J Pharmacol Exp Ther 185: 261-271, 1973.
9.
Chen JS, Walser M. Passive ion fluxes across toad bladder. Biol 18: 365-378, 1974.
J Membr
10.
Idzerda PP, Slegers JFG. Deviating flux rations for Nat in ouabaintreated frog skin. Pfliigers Arch 360: 91-94, 1975.
11.
Schultz SG, Frizell RA, Nellans HN. An eauivalent electrical circuit model for "sodium-transporting" epithelia'in the steady state. J Theor Biol 65: 215-229, 1977.
12.
Lassalles JP, Thellier M. Discussion on the symmetry of macroscopic coefficients in the formulation of the cellu lar fluxes: possible application to a "symmetrical criterion" for the study of active and passive transports. J Theor Biol 68: 53-63, 1977.
13.
Civan MM, Hoffman RE, Effect of aldosterone on electrical resistance of toad 61 adder. Amer J Physiol 220: 324-328, 1971.
14.
Saito
15.
Saito T, Essig A, Caplan SR. The effect of aldosterone on the energetics of sodium transport in the frog skin. Biochim Biophys Acta 318: 371-382, 1973.
T, Essig A. Effect of aldosterone on active and passive conductance and ENa in the toad bladder. J Membr Biol 13: 1-18, 1973.
251
16.
Wiederholt M, Schoormans W, Hansen L, Behn C. Sodium conductance changes by aldosterone in the rat kidney. Pflijgers Arch 348: 155-165, 1974.
17.
Spooner PM, Edelman IS. Further studies on the effect of aldosterone on Biochim Biophys Acta 406: 304electrical resistance of toad bladder. 314, 1975.
18.
Hong CD, Essig A. Effects of 2-deoxy-D-glucose, amiloride, vasopressin, and ouabain on active conductance and ENa in the toad bladder. J Membr Biol 28: 121-142, 1976.
19.
Ziegler TW. A new model for regulation of sodium transport in high Medical Hypotheses 2: 85-96, 1976. resistance epithelia.
20.
Reuss L, Finn AL. Dependence of serosal membrane potential on mucosal membrane potential in toad urinary bladder. Biophys J 15: 71-75, 1975.
21.
Supported by Veterans Administration
252
Research Program.
Hypotheses
5:
247-252,
1979
LIMITATION OF RESISTANCE AS A PARAMETER BY WHICH TO CHARACTERIZE EPITHELIA THAT ACTIVELY TRANSPORT
IONS
Thomas W. Ziegler, Division of Nephrology, Veterans Administration Hospital, San Diego, California 92161 USA and University of California San Diego ABSTRACT It is theoretically inappropriate to characterize an actively transporting epithelium by "resistance" alone which is correctly applied only to passive circuit elements. Rather, such epithelia (if they actively transport sodium) require, as a minimum, characterization by an active circuit element parameter such as voltage (ENa), current (INa) or power (WNa) in some configuration with resistances. Recent experimental studies of epithelia which actively transport sodium have omitted consideration of the active circuit element and attributed all measured changes observed to "resistance" changes in the epithelium as the transepithelial sodium gradient is altered. It is suggested that the observed changes in voltage/current ratio could be consequences of changes in the electrical behavior of the active circuit element of such epithelia. It may be biologically impossible to suppress all electromotive forces in epithelia to measure the truly passive characteristics of the epithelium without destroying tissue viability. The actual methods used to date for measurement of "resistance" in epithelia consist of perturbing signals which might alter the electrical behavior of an active element such as an "ion pump"; the observed changes in voltage to current ratio observed in such experiments can be better explained by a change in the active ion pump rather than by changes in passive epithelial "resistance". Key Words:
epithelial transport, electrophysiology, toad bladder, frog skin, kidney tubule
membrane transport,
DEFINITION Resistance is a parameter used to characterize the physical properties of a conductor. An ohm (the unit of electric resistance) is the electric resistance between two points of a conductor when a constant difference of potential of 1 volt, applied between these two points, produces in this conductor a current of 1 ampere, this conductor not being the source of a 7 electromotive force (1). A conductor is a body incapable ofsupporting electic strain; a charge given to a conductor spreads to all parts of the body (2).
APPLICATION TO EPITHELIAL PHYSIOLOGY Measurements of "membrane resistance" in epithelial physiology ignore both of these definitions:(a) the membrane under study is usually the source of an electromotive force, viz. an ion 'pump" linked to exergonic metabolic reactions within the cell; and (b) biological membranes do continuously support an electric strain manifest as a persisting transmembrane potential Thus, biological membranes which, by virtue of exergonic metaboldifference. ic processes, generate and maintain transmembrane potential differences are not passive circuit elements, rather they are active circuit elements capable of injecting electrical energy into a circuit.
In epithelia which actively transport ions the major flow of ions is polarized in direction to produce the phenomena of secretion or absorption. In selected epithelia (those of the "tight" or non-leaky variety) all or almost all of the ion transport may occur through an electrogenic pathway. Specifically, this is known to occur in the frog skin (3) and toad bladder(4) where the net transepithelial sodium flux equals the short-circuit current. In such tissues, metabolically-linked active ion transport dominates the electrophysiological character of the epithelium. Thus by analogy to circuit theory, the tight epithelium behaves as a battery. Such an active circuit element is characterized by the potential it generates, ENa. A battery or P tight epithelium does possess an "internal resistance" a measure of the frictional loss on movement of electrons through the battery or ions through the epithelium. This loss is dissipated as heat. This "internal resistance" is a secondary or less important characteristic of the battery or tight epithelium and it does not govern the electrical behavior at the battery terminals or at the faces of the epithelium. Rather, for a battery, the E/I ratio observed at its terminals is not a characteristic of the battery itself, but rather is the negative of the resistance of the load applied to the battery. Under open-circuit conditions the battery possesses a characteristic potential E, no current is flowing, so 1=0, and the "resistance" of the battery is E/I = infinity. When the terminals of a battery are short-circuited by a wire of nil resistance, an infinite current would flow, and E/I, theoretically, would equal zero. Practical states of operation of the battery lie somewhere between these two cases and the E/I value for the battery will be the negative of the resistance of the applied load. This number is negative because the current flows through the battery in a direction opposite to the polarity of the battery's voltage. The analogous "load" applied to an actively sodium ion pumping epithelium is the sodium gradient against which the epithelium must deliver ions. Thus, an epithelium pumping sodium ions up a large sodium gradient would appear to have a large amplitude "resistance" or E/I ratio whereas an epithelium delivering sodium ions against a favorable sodium gradient would appear to have a lower amplitude "resistance" or E/I ratio. The value of E/I for the actively transporting epithelium is not a characteristic of the epithelium, but rather of the applied sodium gradient, or load. This explanation may be applied to the studies in toad urinary bladder which showed an increase in "tissue resistance" as mucosal sodium concentration was decreased and a decrease in "tissue resistance" as mucosal sodium concentration was increased (5) and correspondingly converse changes in "tissue resistance" as serosal sodium concentration was altered(6). Similar measurements of transepithelial "resistance" changes have been made 248
in the distal tubule of rat nephron (7). Again, "tissue resistance" decreased as the transepithelial sodium gradient was made more favorable and "tissue resistance" increased as the sodium gradient was made less favorable for transport of sodium. The epithelial "resistance" changes observed were attributed to changes in shunt "resistance", i.e. to structural changes in the epithelium which altered ion flow.
I would suggest that the changes in E/I ratio measured in toad bladder and distal tubule need not be consequences of resistance changes in cell membranes or paracellular pathways but could be better explained as changes in the active circuit element characteristics of the tight epithelia. The E/I value for the actively transporting epithelium is simply the negative of the applied load (sodium gradient). In electrophysiology it is difficult to satisfy the requirement that the conductor under consideration not be the source of any electromotive force. Ion transport processes are integral to cellular integrity and viability and methods which block active transport, such as metabolic inhibitors, may result in artifactual changes in cell membrane resistances. An attempt has been made to study the passive transport characteristics of epithelia after inhibition of the active sodium transport system with ouabain (8,9) but extensive electrophysiological studies have not yet been carried out under these conditions. Although it has not been definitively proven, there is reason to question whether ouabain completely inhibits active transport of sodium in frog skin as sodium does not distribute in accord with the Nernst equation after ouabain (10). Despite extensive theoretical analysis of active vs passive pathways of ion transport (e.g. refs. 11 and 12) most experimental studies of epithelial electrophysiology contain the tacit assumption that the electromotive force of the active transport system remains constant throughout the experimental maneuvers and that measured changes in the E/I ratio are due to passive or resistive changes (5-7, 18). Measurements
of "tissue resistance", though vigorously pursued in the faif to shed light on whether aldosterone stimulates transepithelial sodium transport by decreasing apical membrane resistance, by stimulating the basolateral active pump, by increasing energy delivery to the pump, by a combination of these, or by some other mechanism (13-17). Carefully conducted studies of agents known to modulate sodium transport in epithelia show that measurements of tissue conductance (gN ) (the reciprocal of resistance) do not clarify the site or mode of action o? 2-deoxy-D-glucose, amiloride, vasopressin, or ouabain (18). The latter study concludes that the conductance of the active pathway may dynamically interact with the force of the sodium pump in some fashion, thus gNa and ENa might not be independent variables. Thus, experiments designed to differentiate the locus of action of a drug or hormone on sodium transport as lying at the apical (resistive, passive) barrier for sodium entry or at the basolateral (active) pump step might well be destined to failure.
experimental
Jaboratory,
In analyzing the data from epithelial electrophysiology experiments in the future, I would suggest that actively transporting epithelia be characterized by parameters used to characterize active sources, namely voltage (ENa) or current (INa) in some combination With resistances. Although there is not 249
yet adequate or compelling evidence to require it, I would suggest that biological ion pumps in epithelia may be "work-limited" and that a characteristic "wattage" (WNa) might be the best electrophysiological parameter by which to characterize epithelia. The work accomplished by such transporting epithelia is the sum of the chemical work and the electrical work expended in ion transport. Thus as an epithelium pumps sodium ions against a large, unfavorable sodium gradient it will deliver only a small current, the same epithelium pumping sodium against a smaller, more favorable gradient could deliver a larger current. A "work-limited" ion pump provides a conceptual framework for interrelationship of INa and ENa, and hence provides a possible explanation for gNa and ENa not being independent variables. Interpretation of actual experimental data is facilitated by the assumption of a specific model for epithelial transport. I have suggested a model whereby the "resistive" character of the apical cell membrane and the "active pump character" of the lateral cell membrane are tightly coupled (19). Specifically, this is accomplished by a cytoplasmic sodium "transport pool" of almost infinitesimal size. Experimental demonstration of the electrophysiological character of an ion pump lying in the lateral cell wall of an epithelium will require methods for study which are not yet available. Specifically, it would be necessary to measure sodium activity and potential difference simultaneously in both cellular cytoplasm and adjacent lateral intercellular space fluid as well as ion flux through the pump. Measurement of epithelial resistance has been accomplished in numerous ways, but the method usually consists of application of a perturbing current pulse to the epithelium with measurement of the resulting voltage deflection. It is always tacitly assumed that the amplitude of the perturbing current does not alter the amount of current flowing through the active element of the epithelial cell system being measured (e.g. the "ion pump"). The microelectrode study of Reuss and Finn in the toad bladder (20) shows that the alteration in PD across the basolateral cell membrane follows the alteration in PD across the apical cell membrane within 15 milliseconds when the mucosal sodium entry is perturbed by increment of sodium or addition of amiloride. If the correct explanation for this phenomenon is an infinitesimally small then all measurements of epithelial cytoplasmic sodium "transport pool" (19), resistance made to date use pulses of current of such an amplitude and duration that they could grossly alter sodium activity in this cytoplasmic "transport pool" and thereby alter the electrical behavior of the active "ion pump". CONCLUSIONS (a) It is inappropriate to characterize an actively transporting epithelium by "resistance" alone which is correctly applied only to passive circuit elements; rather it is necessary to include consideration of the active component of ion transport in the analysis of epithelial electro(b) It may be biologically impossible to supphysiological experiments. press all electromotive forces in epithelia to measure the truly passive characteristics of the epithelium without losing the viability and integrity of the tissue; active transport of ions is a sine qua non for cellular viability. (c) Th e actual methods used to measure "rastance" that have been used to date consist of perturbing signals which might alter the 250
electrical behavior of the active ion pump in epithelia rather than serving as a "probe" of the passive, resistive components of the epithelia. REFERENCES 1.
Weast RC, editor. Handbook of Chemistry and Physics, 55th edition, CRC Press, Cleveland, Ohio, 1974-1975, p. F-119.
2.
ibid., p. F-88.
3.
Ussing HH, Zerahn K. Active transport of sodium as the source of electric current in the short-circuited isolated frog skin. Acta Physiol Stand 23: 110-127, 1951.
4.
Frazier HS, Leaf A. The electrical characteristics of active sodium transport in the toad bladder, J Gen Physiol 46: 491-503, 1963.
5.
Reuss L, Finn AL. Effects of changes in the composition of the mucosal solution on the electrical properties of the toad urinary bladder epithelium. J Membr Biol 20: 191-204, 1975.
6.
Finn AL, Reuss L. Effects of changes in the composition of the serosal solution on the electrical properties of the toad urinary bladder epithelium. 3 Physiol (Lond) 250: 541-558, 1975.
7.
OeBermudez L, Windhager EE. Osmotically induced changes in electrical resistance of distal tubules of rat kidney. Amer J Physiol 229: 1536-1546, 1975.
8.
Walser M, Hammond V, Butler S. Depolarization increases susceptibility of toad bladder sodium transport to inhibition by ouabain. J Pharmacol Exp Ther 185: 261-271, 1973.
9.
Chen JS, Walser M. Passive ion fluxes across toad bladder. Biol 18: 365-378, 1974.
J Membr
10.
Idzerda PP, Slegers JFG. Deviating flux rations for Nat in ouabaintreated frog skin. Pfliigers Arch 360: 91-94, 1975.
11.
Schultz SG, Frizell RA, Nellans HN. An eauivalent electrical circuit model for "sodium-transporting" epithelia'in the steady state. J Theor Biol 65: 215-229, 1977.
12.
Lassalles JP, Thellier M. Discussion on the symmetry of macroscopic coefficients in the formulation of the cellu lar fluxes: possible application to a "symmetrical criterion" for the study of active and passive transports. J Theor Biol 68: 53-63, 1977.
13.
Civan MM, Hoffman RE, Effect of aldosterone on electrical resistance of toad 61 adder. Amer J Physiol 220: 324-328, 1971.
14.
Saito
15.
Saito T, Essig A, Caplan SR. The effect of aldosterone on the energetics of sodium transport in the frog skin. Biochim Biophys Acta 318: 371-382, 1973.
T, Essig A. Effect of aldosterone on active and passive conductance and ENa in the toad bladder. J Membr Biol 13: 1-18, 1973.
251
16.
Wiederholt M, Schoormans W, Hansen L, Behn C. Sodium conductance changes by aldosterone in the rat kidney. Pflijgers Arch 348: 155-165, 1974.
17.
Spooner PM, Edelman IS. Further studies on the effect of aldosterone on Biochim Biophys Acta 406: 304electrical resistance of toad bladder. 314, 1975.
18.
Hong CD, Essig A. Effects of 2-deoxy-D-glucose, amiloride, vasopressin, and ouabain on active conductance and ENa in the toad bladder. J Membr Biol 28: 121-142, 1976.
19.
Ziegler TW. A new model for regulation of sodium transport in high Medical Hypotheses 2: 85-96, 1976. resistance epithelia.
20.
Reuss L, Finn AL. Dependence of serosal membrane potential on mucosal membrane potential in toad urinary bladder. Biophys J 15: 71-75, 1975.
21.
Supported by Veterans Administration
252
Research Program.
