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Ionic exchanges and cardiac action potential inrelation to the electrocardiogram
Ionic Exchanges and Cardiac Action Potential in Relation to the Electrocardiogram By STANLEY A. BRILLER* H E SURVIVAL of a living cell depends upon its ability to sequester find to protect its enzymes, genetic material and other complex protein molecules. Cell walls or membranes, through wlfich relatively large molecules cannot pass, insure that these precious substances will not drift away. The osmotic consequence of such partitioning is tlle movement of water and solute into the cell, causing swelling and the threat of rupture. 1 Tlfis osmotic process as well as tlle cellular meclmnism for avoiding its grim results bring about a unique separation of tlm univalent ions of the intra- and extracellular compartments. Such an ionic separation is associated with tile creation of a difference in electrical potential across the cell membrane. Tile relationshi p between the electrical potential or voltage and the ionic milieu on tlle two sides of the cell membrane may most easily be understood by examining the .effects of connecting a battery to two electrodest which dip into two compartments of a container separated by an inert, semipermeable membrane (fig. 1). If the compartments on either side of the membrane contain equimolar concentrations of a salt such as KC1, it is apparent that the potassium cations will be attracted to the compartment containing the negative electrode whereas chloride anions will proceed to the positive electrode. It can be appreciated that after a given amount of time the concentration of potassium surrounding the cathode would be much greater than that about the anode (fig. 2). An opposite situation obviously applies to the disposition of the chloride ion. The point at which no further separation of these ion species can be attained is a fimction of the voltage applied. This relationship is defined by the Nernst equation:
T
RT Qt E = ---Loge ~ ZF Q.,
equation1
where E is the battery potential, R is the gas constant (1.987 calories per mole per degree), T is tlm absolute temperature, Z is the valency, F the Farad (96,500 coulombs per equivalent), e is the natural logarithmic base, and QI and Q., are the ionic concentrations in compartments i and 2 respectively. This equation may be applied to anions as well as cations. As printed, it will relate the polarity detected in the "Q~" compartment to the cationic concentration ratio. The sign must be changed if predictions due to anionic displacement are to be made, or if cationic measurements are made in the *Established Investigator, American Heart Association. tThese are hypothetical electrodes, with the following properties: (1) Both anode and cathode create a uniform cquipotential throughout the volume of each compartment into which they dip so that the potential gradient exists solely across the membrane; (9.) no chemical action occurs at either electrode. 207
008
STANLEY A. BRILLER
-IlJl,II
-I
B K÷ CL-
D
All ÷
o~-
CLK÷
"
FIG. 1.--Disposition of potassium and chloride ions at instant of excitation of hypoflletical electrodes described in text. Vertical dashed line represents semipermeable membrane. Horizontal arrows indicate net ion current or flux. Dashes within electrodes indicate relative electron charge. (After Briller, S. A.: Ionic basis of the transmembrane potential. In Kossman, C., Ed.:.Advances in Electrocardiography. New York, Grune & Stratton, 1958.)
,h K÷
GL-
CL-
K÷
FIG. 2.--Disposition of potassmm and cldoride ions whose concentrations are in equilibrium with battery voltage. Absence of flux arrows indicates zero net ionic flux. (After Briller, S. A.: Ionic basis of the transmcmbrane potential. In Kossman, C., Ed.: Advances in Electrocardiography. New York, Grune & Stratton, 1958.) "Q.~" compartment. Although the following discussion applies with equal validity to both anions and cations, for simplicity only the potential measured in compartment "QI" due to the cationic distribution (potassium ion) will be described. Movements and c o n c e n t r a t i o n of chloride are opposite but equal to those of potassium in this case. It should be noted that in the example cited equation 1 applies only after a steady state of differential concentratiolis fias been attained. W h e n the battery is first switched on, the concentrations of potassium within the compartments are equal and the calculated voltage ( 0 ) d o e s n o t agree with t h a t a p p l i e d. Accordingly it is necessary to apply equation i only after equilibrium has been reached or to add expressions for the movement or flux of the ions across the membrane:
IONIC EXCIIANfiESAND CARDIACACTION POTENTIAL
RT
009
Q1F1
equation2
E = --~ Loge ~ ZF o2eo
The symbolization in equation 2 is similar to that in equation 1. Fx represents tlow toward Q1, F.~ flow in the opposite direction (fig. 3). When the battery in figure 1 is switched on, Fx greatly exceeds F_% and tile equation will predict the voltage of tile batter), although tile concentrations of ions have not had time to change appreciably. If the battery is disconnected from this equilibrated system, the ions tend to flow in such a direction that equal concentrations of ions in both compartments ultimately will be obtained. The polarity is unchanged. In the case of potassium ion in the model system, the flux ratio reverses, i.e., F2 becomes greater than Fa. Since the flux ratio is disposed oppositely to the concentration ratio, the potential will be somewhat less than when F1 was equal to F2 in the equilibrium state. It is conceivable that if a battery be connected to this system in such a manner that the negative pole is attached to the "Q2" compartment, potassium ions will be driven out of the "QI" compartment at a greater rate than that at which they naturally tend to flow. Under these circumstances, the flux ratio will exceed the inverted concentration ratio and the polarity of the system will be reversed. The preceding discussion may be summarized as follows: (1) The polarity of an equilibrated or balanced ionic system will be the opposite of the charge of the most highly concentrated ion contained in the compartment in which the measurement is made. (2) If energy is delivered to such a system, the net flow will be toward the greatest or potentially greatest concentration of ion species, until equilibrium is reached. (3) If the system is delivering energy, the net ionic flow will be away from the most concentrated ionic milieu. The potential will be lower in this case than in the equilibrium state. (4) If energy is supplied to a system in such a way that the flow away from the more concentrated environment is hastened, the polarity may be reversed.
FI~
Q~
FI
FIG. 3.--Symbolic representation of equation 2 at equilibrium. (After Briller, S. A.: Ionie basis of the transmembrane potential. In Kossman, C., Ed.: Advances in Electrocardiography. New York, Grune & Stratton, 1958.)
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STANLEY A. BRILLER
It has been assumed for tile model system that there was a known and fixed value of membrane permeability for potassium ion. However, it must be appreciated that another species of ion might have more or less difficulty in penetrating such a membrane by virtue of a difference in size compared to potassium. Moreover, as will be seen, a membrane may at times vary in its physical ability to restrain specific ionic movement. In general, if several ionic systems are compared, that in which the permeabilities are greatest can supply the greatest ionic current or flux. The freely moving ion in a complex system may thus swamp effects due to more sluggish members of tlle population. An ion which is incapable of penetrating a membrane cannot per se contribute to an ionic current although it generally will bring about a redistribution of other permeant ions. It must be stressed that the battery-electrode models discussed thus far cannot be physically constructed. They are "thought experiments" devised to demonstrate some of tlle variables which determine the magnitude and polarity of voltages appearing across membranes, living and otherwise. TtIE RESTING BIOLOGIC SYSTE.Xl
The distribution ratios of potassium and chloride on either side of a living cell membrane (fig. 4) approximate the ionic separation that would be expected if a 90 millivolt battery were connected to the hypothetical system described above. Intracellular, negatively charged protein which cannot permeate the cell membrane has .long been regarded as the "battery" of the biologic system. If the potassium salt of a protein is placed on one side of a membrane and potassium chloride is added, the system will be in equilibrium when the distribution of the ionic constituents identified in figure 5 corresponds to the following equation: x 2 -- y ( y + z )
eqtmtion 3
For example, if three equivalents each of protein (z) and potassium (z) in the form of a potassium proteifiate were placed on one side of a simple membrane and three equivalents each of potassium (x+y) and chloride (x+y) were added, the transmembrane ratios of these substances at equilibrium would be as follows: protein anion 3:0 (z:0); potassium ion 4:2 (z+y:x); chloride ion 1:2 (x:y). Donnan showed that these distributions were to be anticipated from tlle laws of thermodynamics, which demand electrical neutrality on each side of the membrane.-" It will be noted that the transmembrane ratios of the diffusible elements of this system may be expected to produce a transmembrane potential difference whose magnitude should be predicted by equation 1. There is considerable evidence that this prognostication is valid: 1. A microelectrode inserted into' the interior of a muscle or nerve fiber measures a potential of about 90 millivolts negative with respect to the exterior of the cell. A potential of this magnitude is i n fairly good agreement with calculated values utilizing equation 1 and the actual intra- and extracellular concentration of chloride or potassium. 2. If tlie external concentration of potassium is clmnged, except for low
211
I O N I C E X C t l A N G E S A N D CARDIAG A C T I O N P O T E N T I A L
IN TRACEL L LIL AR
EX TRAC,ELLULAR
I PROTEIN-] CL"
cC
+
K
K
NA ÷
FIc. 4.--Relative concentrations of certain ionic constituents of the intra- and extracellular spaces. (After Briller, S. A.: Ionic basis of the transmembrane potential. In Kossman, C., Ed.: Advances in Electrocardiography. New York, Grune & Stratton, 1958.)
membrane z PROTEINz + y K+
y CL-
K+
x
CL-
x
Fie. 5.--Concentrations (x, y and z) in equivalents of constituents of Donnan equilibrium. See text and equation 3. values of external potassiuin, tile observed potentials agree almost exactly with the potential calculated with equation 1, in which the internal concentration of potassium is constant, but in which the experimentally varied values of tile external concentration are inserted. 3 In such experiments, suflqcient time must be allowed for a new flux equilibrium to be achieved after the extracellular potassium concentration is altered. 4 It is assumed that any net gain or loss of intracellular potassium is accompanied b y similarly directed water movement, permitting the concentration of intracellular potassium to remain unaltered. 3. T h e presumption of flux equilibrium for potassiuin has been confirmed by the use of radioactive tracer studies. '~ Although these experiments were performed on isolated tissue in which there is an apparently Unavoidable
212
STANLEY
A. B R I L L E R
loss of potassium, the calculated agrees with tlle measured potential ~,hen the flux inequality is introduced into equation 2. 4. The foregoing experiments indicate that potassium penetrates the cellular membrane freely. 5. Chloride ion acts in a manner eniirely comparable to potassium. G In addition to the electrical effects discussed above, the two compartments of a simple Donnan system will generally be at different pressures. At equilibrium, the compartment containing tile nondiffusing ion (protein) will contain the greater number of particles. Such an osmotic imbalance results in a shift of water to tlle protein-containing compartment. This water shift and subsequent rise in pressure within tile protein (intracellular) compartment may be avoided by adding sufficient nondiffusing solute to the protein-free (extracellular) compartment. Tile concentration of sodium ion in tile extracelhdar space is sufficient to produce isosmolarity with the intracellular compartment. However, this ion has been shown to play a far more dynamic role than that of a passive, impermeable solute. It has been found that although tile cell membrane is some 30 times less permeable to sodium titan to potassium ion, the former passes across the membrane in considerable numbers, r Hence the resting cell membrane cannot be thought to be impermeable to sodium. Reference to equation 2 reveals that by its concentration ratio alone, the low intracellular and high extracellular concentrations of sodium might be thought to produce a potential whose polarity is tile opposite of that observed. There is only one way to reconcile this paradox in view of the appreciable permeability of tile membrane to sodium: the inward flux (F1) of sodium ion must be 50 to 100 times that of the outward flux (F~). Radiotracer studies, however, have revealed a ratio many times smaller.~ Indeed, these studies confirm the fact that the intact resting cell must be in sodium balance. If it is presumed that the inward flux of sodium is an ionic one, but that an equivalent amount of sodium is "sneaked" across ttle membrane in complex form, the ioliic flux ratio would agree with the predicted ratio. The exact manner in which sodium might be expelled from a cell is not known. Terms such as "active transport" and "sodium pump" lmve been used to describe the process. A theoretical sclieme outlined by one group of investigators s is presented in figure 6. Here an intracellular substance "P" combines with intracellular sodium ion and the combination passes across the membrane in complexed form. In the extracellular compartment, dissociation of tlle P N a + cbmbination is much favored by tile great affinity of ground substance (GS) f o r P . Sodium ion is thereby free to rediffuse into the cell. The other constituefits ot~ the extra- and intracellular compartments are distributed in accord \vith the-potefitial developed by the active transport or pumping of sodium arid the Donnan equilibrium. On the basis of its physical and chemical properties and its distribution in tissue, histamine has been proposed as being a likely "pump substance. "D It might be added that serotonin is at least as likely a candidate. Whatever the mechanism responsible for the extrusion of intracellular sodium ion, it appears that metabolic energy is introduced at this point. Whether it is ex-
213
IONIC EXCtIANGES AND CARDLa.CACTION POTENTIAL
CL-
c4J'el.-
PROTEIN-
NA.P Gs pG S ÷
K+
l~t÷
[K+ K÷
FIG. 6.--Equilibria across resting cell membrane (rectangle). P is pump substance,..GS is extracellular ground substance. Dashed arrow represents flux of sodium in complexed form. (After Briller, S. A.: Ionic basis of the transmembrane potential. In Kossman, C., Ed.: Advances in Electrocardiography. New York, Grune & Stratton, 1958.)
pended in the synthesis of a "pump substance" or in some other modality is a matter of much speculation. Tile sodium pump, in summary, can be viewed (1) as a dynamic osmoregulator which prevents the accumulation of intracellular sodium and water and (2) as a Donnan mechanism complement .with which rapid adjustment of the transmembrane potential can be made in response to activity and stress. Activity of the sodium pump would appear to account for the following facts: (1) significant changes in the resting potential of nerve cells are not obtained after the microinjection of potassium in amounts sufficient to produce a calculated change of about 33 per cent lo., (2) the natnre of the electrodes used to measure the resting potential appears to have..little effect on tile magnitude of the voltage detected. If a Donnan equilibrium were the sole source of the resting potential, no voltage should be detectable with the unmodified silver-silver chloride electfodes used in this w°rkl°; (3) the internal/external potassium ratio differs significantly from the external/internal chloride ratio although these ratios'should be identical according to classical Donnan theory. 1° .... It is of interest that there may be an alternative explanation for the'lastcited observation. StSmpfli has recently shown that potassium perm'eabi.lity of nerve may be dependent upon the magnitude . . . . of the restingp6[ential. 11=~,. . When the latter is large the potassium permeabdlty is suddenly and ~significantly reduced. It is implied that the resting potehtial of intact tissue 'i~ dependent chiefly upon the transmembrane chloride ratio. Under t h e s e con'-¢: ditions variation of the extracellular potassium ratio would have little effect upon the resting potential. However, even minimal trauma t ° the tissue under study may reduce the resting potential sufficiently to augment potassium permeability a n d in effect switch on the potassium '¢battery."
214
STANLEY A. BRILLER
TIIE ACTIVEBIOLOGICSTATE Maintenance of the resting potential of a cell has been shown to represent a manifestation of the expenditure of metabolic energy in bringing about a unique separation of the monovalent ionic constituents of the cell. The active state will be seen to demonstrate the results of allowing this separation to lapse in a carefully integrated manner. Hodgkin, Huxley and Katz ~-° demonstrated that the greater impermeability of the resting membrane of an axon to sodium can be abruptly abolished by reducing the resting potential electrically. Such a reduction in potential may be brought about by a natural or artificial pacemaker or by currents from adjacent active cells. The effect of allowing freer flux of sodium ion across the cell membrane (which maintains its resting semipermeability to potassium) is that the sodium pump mechanism becomes overwhelmed. Consequently there is relatively free movement of sodium ions in both directions across the membrane although inward movement of this ion predominates. ~ Unrestrained sodium movement impelled by its concentration gradient is therefore able to deliver free energy to the cell in the form of electrical potential which tends to make the inside of the cell less negative. Such a change in potential in turn makes the membrane more permeable to sodium and, coupled with the presumed inactivation of the sodium pump mechanism, the intracelhdar potential rises past zero toward the level p r e d i c t e d b y equation 1 for sodium ion. r It should be noted that during this process the cell gains a number of sodium ions. However, the net gain is but an infinitely small proportion of the sodium already there23 As the movements of sodium ions across the membrane reach a peak (at which time the intracellular potential is positive in polarity) the membrane gradually begins to increase in permeability to potassium. These latter ions, impelled by the hostile positively charged intracellular environment, leave the cell in numbers greater than the number of entering potassium ions. These free movements of potassium (coupled with the now decreasing permeability of the membrane to sodium) reduce the positive potential within the cell. Finally, as the impermeability of the membrane to sodium is completely re-established, potassium equilil)rium potential dominates once again and the intracellular potential resumes its negative polarity. During the later phases of the "active state," the potassium permeability gradually declines to its previous level. Such changes in sodium and potassium permeability and intracellular potential for a nerve celP 4 are shown in figure 7. It will be recalled that the cell has gained sodium and lost potassium in passing through the active state. Reactivation of the sodium pump with subsequent extrusion of sodium coupled with re-entry of potassium occurs promptly 1~ and is synchronous with ~;arying degrees of nonresponsiveness of the cellular mechanism known as the absolute and relative refractory periods. The large size of certain axons, the simplicity of their geometric form and, most of all, the ability of a nerve cell to pass through its active phase without moving have made it possible to document the foregoing ionic behavior of
215
I O N I C E X C I I A N G E S A N D CARDIAC A C T I O N P O T E N T I A L
90
35-
F
P
30-
70
25 50
40
-
20 _-:-
-
3020lo;ok
x
g
T 3
o msec.
I 35
t 4--"
"----
Fie. 7.--Calculated action potential V and ionic eonductances (gK potassium, g.~a sodium, g total condnctance) of a propagated nerve impulse. (From ttodgkin, A. L., and Huxley, A. F.: A quantitative description of membrane current and its application to conduction and excitation in nerve. J.Physiol. 117:500, 1952.) this tissue with precision. Repetition of similar direct studies in a single myocardial fiber has been impossible thus far. Although there is little reason to snspect that there are basic differences in tile generation of the resting potential in a myocardial fiber and in nerve, there are unique features of the active myocardial process: (1) Except for similar speed and magnitude of tile upstroke, tile morphologies of action potentials of myocardial (fig. 8) and nerve cells (fig. 7) differ vastly. The total duration of the action potential of a myocardial cell may be several hundred times that of a nerve cell. (2) Although the time variation of the total membrane condnctance of an active nerve is a fairly smooth monophasie curve (fig. 7), 1~ a plot of the same parameter in a kid Purkinje fiber (fig. 8) 16 is triphasic. These observations suggest that depolarization in laeart muscle and in nerve is due to similar mechanisms: a regenerative relationship between (a) reduction in resting potential by adjacent cells, (b) increases in membrane permeability to sodium and (c) net entry of this ion into tile fiber. Presumed decline of active transport a n d hyperpermeability of ionic sodium (documented by a synchronous increase in membrane conductivity) permit the peak of tile action potential to approach the positive equilibrium voltage predicted by equation 1 for the transmembrane concentrations of sodium. Although the action potential falls fairly rapidly at first (phase I), it hovers about zero potential for several hundred milliseconds (phase II) at a time when the total membrane conductance abruptly decreases. These values of potential and total membrane conductance can be explained o n l y by a decline in potassium conductance which greatly exceeds a simultaneous diminution in sodium conductance, lr Since the intracellular potential at this time can be expected to force potassium out of the cell, a decline ih potassium conductance would serve to minimize loss of this ion to the extracellular space. Indirect confirmation of this premise has been obtained by Conn and Wood, who found that in the isolated, perfused dog heart, tile
216
A. BRILLER
STANLEY
o II
I
| 5, I
H
,mV
!
I I
2o
I I I
o
gtotal
-2( -.0
-4( -6C -8C
II
9.01
I
I
I
I
I
I
0.5 S E C O N D
I
I
I
I
901
I
Fic. 8.--Action potential (with phases I, II and III of repolarization identified between vertical dashed lines) of kid Purkinje fiber. Simultaneous values of total membrane conductance (gtotal) in relative units. Conductance values calculated from membrane resistance measurements of \VeidmannJ c (Adapted from Weidmann, S.: Resting and action potentials of cardiac muscle. Ann. New York Acad.Sc. 65:663, 1957.) exchange rate of potassium was one-half that of sodium, is The pulsatile nature of the potassium efltux in the turtle heart has been noted by others1? and may be greatest during phase III of repolarization when the total membrane conductance increases to near-diastolic levels. Since artificial enrichment of extracellular potassium is known to shorten the duration of the action potential of heart muscle, the natural extracellular accumulation of this ion as a result of depolarization is believed to initiate the repolarization process. 16 Active extrusion of the previously accumulated sodium coupled with the re-entry of lesser amounts of potassium would then serve to complete the cycle. There is the possibility that these latter events begin during phase III of repolarization. As applied to electrocardiography in a qualitative sense, the QRS deflections take origin from free, transmembrane movements of sodium ions whereas the T wave is probably ascribable to comparable activity of potassium.
IONIC F~XCIIANGESAND CARDIACACTION POTENTIAL
~0~7
The crux of the mechanism of tim action potential is the ability of the cell membrane to undergo tile required serial, selective changes in permeability to sodium and potassium ions. Although calicum ion, a most necessary ingredient for nerve and muscle function, apparently plays no direct role in generating the transmembrane potential, it is believed to be active in regulating membrane permeability, s Wilson and Nachmansohn 2° believe that acetylcholine is implicated in causing alterations in the molecular structure of the membrane during activity. Others 7 indicate that the amount of heat generated during activity is too small to suggest an origin other than that due to movement of ions through the membrane. A functional, submicroscopic view of the biologic membrane theoretically would reveal (a) pores through which ions pass and (b) intervening, totally impermeable areas of membrane substance. The electrical analogs of (a) and (b) are a resistance and a capacitor, respectively. Studies of the alterations in cell membrane impedance during the action potential have shown that the capacitance of the membrane is constant. -°~ These observations strengthen the contention that changes in membrane permeability do not imply structural alterations, and direct attention to the pore moiety. In this light, studies of artificial membranes carrying fixed charges presumably on their pore walls are of considerable interest. Sollner et al. have shown that such membranes may discriminate between sodium and potassium ions. ~°z Only future work can determine whether such charged pores exist within biologic membranes and; moreover, whether these charges are time-dependent fimctions of the membrane voltage as required by the Hodgkin-Huxley thesis. ~4 The latter theory is an elegant mathematical expression of the relationship between the action potential and the various ionic currents of a squid axon; the ideas expressed in it underlie much of tim discussion of the active biologic state in this article. REFERENCES 1. Leaf, A.: Maintenance of concentration during nervous activity. J.Physioh gradients and regulation of cell vol114:119, 1951. ume. Ann. New York Acad.Sc. 72: 6. Ussing, H. H.: Ion transport across 396, 1959. biological membranes. In Clarke, H. 2. Donnan, F. G.: Theorie der MembranT., Ed.: Ion Transport Across Memgleichgewichte und Membranpotenbranes. New York, Academic Press, tiale bei Vorhandenseln von Nicht 1954, p. 3. Dialysierenden Elektrolyten. Ein 7. Hodgkln, A. L.: The ionic basis of elecBeitrag zur Physikalisch-Chemiscben trical activity in nerve and muscle. Physiologic. Zeitschrift Fur ElcktroBiol.Rev. 26:339, 1951. chcmle 17:572, 1911. 8. Parlin, R. B.: Membrane permeability 3. Boyle, P. J., and Conway, E. J.: Potasand electrical potcntial.. In Clarke, sium accumulation in muscle and H. T., Ed.: .Ion Transport Across associated changes. J.Physiol. 100:1, Membranes. New York, Academic 1941. Press, 1954, p. 103. 4. Conway, E. J.: Nature and significance 9. Eyring, H., and Dougherty, T. F.: of concentration relations of potasMolecular mechanisms in inflammasium and sodium ions in skeletal tion and stress. Am. Scientist 43:457, muscle. Physiol.Rev. 37:84, 1957. 1955. 5. Keynes, R. D.: The ionic movements 10. Grundfest, H.: The nature of the elec-
218
11. 12.
13.
14.
15.
16.
17.
STANLEY A. BRILLER trochcmical potential of bioclectrie tissue. In Shedlovsky, T., Ed.: Electrocbemistry in Biology and Medicine. New York, John Wiley & Sons, 1955, p. 141. Sffimpfli, R.: Personal communication. Hodgkin, A. L., Huxley, A. F., and Katz, B.: Measurement of current voltage relations in the membrane of tim giant axon of Loligo. J.Physiol. 116.'424, 1952. Keynes, R. D., and Lewis, P. R.: The sodium and potassium content of cephalopod nerve fibers. J.Physiol. 114:151, 1951. Hodgkin, A. L., and Huxley, A. F.: A quantitative description of membrane current and its application to conduction and excitation in nerve. J.Physiol. 117:500, 1952. - - , and Keynes, R. D.: Active transport of cations in giant axons from Sepia and Loligo. J.Physiol. 128:28, 1955. Weidmann, S.: Resting and action potentials of cardiac muscle. Ann. New York Acad.Sc. 65:663, 1957. Brady, A. J., .and Woodbury, J. W.: Effects of sodium and potassium on
18.
19.
20.
21.
22.
repolarization in frog ventricular fibers. Ann. New York Acad.Sc. 65: 687, 1957. Conn, H. L., and Wood, J. C.: Cation exchanges in tlle heart: relation to tile cardiac action potential. J.Clin. Invest. 37:885, 1958. Wilde, W. S.: Tile pulsatile nature of the release of potassium from heart muscle during the systole. Ann. New York Acad.Se. 65:693, 1957. Wilson, I. B., and Nachmansohn, D.: Tile generation of bioelectrie potentials. In Clarke, H. T., Ed.: Ion Transport Across Membranes. New York, Academic Press, 1954, p. 35. Cole, K. S., and Curtis, H. J.: Electric impedance of the squid giant axon during activity. J.Gen.Physiol. 22: 671, 1939. Sollner, K., Dray, S., Grim, E., and Neihof, R.: Membranes of high electrochemical activities in studies of biological interest. In Shedlovsky, T., Ed.: Electrochemistry in Biology and Medicine. New York, Jolm Wiley & Sons, 1955, p. 65.
T
RT Qt E = ---Loge ~ ZF Q.,
equation1
where E is the battery potential, R is the gas constant (1.987 calories per mole per degree), T is tlm absolute temperature, Z is the valency, F the Farad (96,500 coulombs per equivalent), e is the natural logarithmic base, and QI and Q., are the ionic concentrations in compartments i and 2 respectively. This equation may be applied to anions as well as cations. As printed, it will relate the polarity detected in the "Q~" compartment to the cationic concentration ratio. The sign must be changed if predictions due to anionic displacement are to be made, or if cationic measurements are made in the *Established Investigator, American Heart Association. tThese are hypothetical electrodes, with the following properties: (1) Both anode and cathode create a uniform cquipotential throughout the volume of each compartment into which they dip so that the potential gradient exists solely across the membrane; (9.) no chemical action occurs at either electrode. 207
008
STANLEY A. BRILLER
-IlJl,II
-I
B K÷ CL-
D
All ÷
o~-
CLK÷
"
FIG. 1.--Disposition of potassium and chloride ions at instant of excitation of hypoflletical electrodes described in text. Vertical dashed line represents semipermeable membrane. Horizontal arrows indicate net ion current or flux. Dashes within electrodes indicate relative electron charge. (After Briller, S. A.: Ionic basis of the transmembrane potential. In Kossman, C., Ed.:.Advances in Electrocardiography. New York, Grune & Stratton, 1958.)
,h K÷
GL-
CL-
K÷
FIG. 2.--Disposition of potassmm and cldoride ions whose concentrations are in equilibrium with battery voltage. Absence of flux arrows indicates zero net ionic flux. (After Briller, S. A.: Ionic basis of the transmcmbrane potential. In Kossman, C., Ed.: Advances in Electrocardiography. New York, Grune & Stratton, 1958.) "Q.~" compartment. Although the following discussion applies with equal validity to both anions and cations, for simplicity only the potential measured in compartment "QI" due to the cationic distribution (potassium ion) will be described. Movements and c o n c e n t r a t i o n of chloride are opposite but equal to those of potassium in this case. It should be noted that in the example cited equation 1 applies only after a steady state of differential concentratiolis fias been attained. W h e n the battery is first switched on, the concentrations of potassium within the compartments are equal and the calculated voltage ( 0 ) d o e s n o t agree with t h a t a p p l i e d. Accordingly it is necessary to apply equation i only after equilibrium has been reached or to add expressions for the movement or flux of the ions across the membrane:
IONIC EXCIIANfiESAND CARDIACACTION POTENTIAL
RT
009
Q1F1
equation2
E = --~ Loge ~ ZF o2eo
The symbolization in equation 2 is similar to that in equation 1. Fx represents tlow toward Q1, F.~ flow in the opposite direction (fig. 3). When the battery in figure 1 is switched on, Fx greatly exceeds F_% and tile equation will predict the voltage of tile batter), although tile concentrations of ions have not had time to change appreciably. If the battery is disconnected from this equilibrated system, the ions tend to flow in such a direction that equal concentrations of ions in both compartments ultimately will be obtained. The polarity is unchanged. In the case of potassium ion in the model system, the flux ratio reverses, i.e., F2 becomes greater than Fa. Since the flux ratio is disposed oppositely to the concentration ratio, the potential will be somewhat less than when F1 was equal to F2 in the equilibrium state. It is conceivable that if a battery be connected to this system in such a manner that the negative pole is attached to the "Q2" compartment, potassium ions will be driven out of the "QI" compartment at a greater rate than that at which they naturally tend to flow. Under these circumstances, the flux ratio will exceed the inverted concentration ratio and the polarity of the system will be reversed. The preceding discussion may be summarized as follows: (1) The polarity of an equilibrated or balanced ionic system will be the opposite of the charge of the most highly concentrated ion contained in the compartment in which the measurement is made. (2) If energy is delivered to such a system, the net flow will be toward the greatest or potentially greatest concentration of ion species, until equilibrium is reached. (3) If the system is delivering energy, the net ionic flow will be away from the most concentrated ionic milieu. The potential will be lower in this case than in the equilibrium state. (4) If energy is supplied to a system in such a way that the flow away from the more concentrated environment is hastened, the polarity may be reversed.
FI~
Q~
FI
FIG. 3.--Symbolic representation of equation 2 at equilibrium. (After Briller, S. A.: Ionie basis of the transmembrane potential. In Kossman, C., Ed.: Advances in Electrocardiography. New York, Grune & Stratton, 1958.)
210
STANLEY A. BRILLER
It has been assumed for tile model system that there was a known and fixed value of membrane permeability for potassium ion. However, it must be appreciated that another species of ion might have more or less difficulty in penetrating such a membrane by virtue of a difference in size compared to potassium. Moreover, as will be seen, a membrane may at times vary in its physical ability to restrain specific ionic movement. In general, if several ionic systems are compared, that in which the permeabilities are greatest can supply the greatest ionic current or flux. The freely moving ion in a complex system may thus swamp effects due to more sluggish members of tlle population. An ion which is incapable of penetrating a membrane cannot per se contribute to an ionic current although it generally will bring about a redistribution of other permeant ions. It must be stressed that the battery-electrode models discussed thus far cannot be physically constructed. They are "thought experiments" devised to demonstrate some of tlle variables which determine the magnitude and polarity of voltages appearing across membranes, living and otherwise. TtIE RESTING BIOLOGIC SYSTE.Xl
The distribution ratios of potassium and chloride on either side of a living cell membrane (fig. 4) approximate the ionic separation that would be expected if a 90 millivolt battery were connected to the hypothetical system described above. Intracellular, negatively charged protein which cannot permeate the cell membrane has .long been regarded as the "battery" of the biologic system. If the potassium salt of a protein is placed on one side of a membrane and potassium chloride is added, the system will be in equilibrium when the distribution of the ionic constituents identified in figure 5 corresponds to the following equation: x 2 -- y ( y + z )
eqtmtion 3
For example, if three equivalents each of protein (z) and potassium (z) in the form of a potassium proteifiate were placed on one side of a simple membrane and three equivalents each of potassium (x+y) and chloride (x+y) were added, the transmembrane ratios of these substances at equilibrium would be as follows: protein anion 3:0 (z:0); potassium ion 4:2 (z+y:x); chloride ion 1:2 (x:y). Donnan showed that these distributions were to be anticipated from tlle laws of thermodynamics, which demand electrical neutrality on each side of the membrane.-" It will be noted that the transmembrane ratios of the diffusible elements of this system may be expected to produce a transmembrane potential difference whose magnitude should be predicted by equation 1. There is considerable evidence that this prognostication is valid: 1. A microelectrode inserted into' the interior of a muscle or nerve fiber measures a potential of about 90 millivolts negative with respect to the exterior of the cell. A potential of this magnitude is i n fairly good agreement with calculated values utilizing equation 1 and the actual intra- and extracellular concentration of chloride or potassium. 2. If tlie external concentration of potassium is clmnged, except for low
211
I O N I C E X C t l A N G E S A N D CARDIAG A C T I O N P O T E N T I A L
IN TRACEL L LIL AR
EX TRAC,ELLULAR
I PROTEIN-] CL"
cC
+
K
K
NA ÷
FIc. 4.--Relative concentrations of certain ionic constituents of the intra- and extracellular spaces. (After Briller, S. A.: Ionic basis of the transmembrane potential. In Kossman, C., Ed.: Advances in Electrocardiography. New York, Grune & Stratton, 1958.)
membrane z PROTEINz + y K+
y CL-
K+
x
CL-
x
Fie. 5.--Concentrations (x, y and z) in equivalents of constituents of Donnan equilibrium. See text and equation 3. values of external potassiuin, tile observed potentials agree almost exactly with the potential calculated with equation 1, in which the internal concentration of potassium is constant, but in which the experimentally varied values of tile external concentration are inserted. 3 In such experiments, suflqcient time must be allowed for a new flux equilibrium to be achieved after the extracellular potassium concentration is altered. 4 It is assumed that any net gain or loss of intracellular potassium is accompanied b y similarly directed water movement, permitting the concentration of intracellular potassium to remain unaltered. 3. T h e presumption of flux equilibrium for potassiuin has been confirmed by the use of radioactive tracer studies. '~ Although these experiments were performed on isolated tissue in which there is an apparently Unavoidable
212
STANLEY
A. B R I L L E R
loss of potassium, the calculated agrees with tlle measured potential ~,hen the flux inequality is introduced into equation 2. 4. The foregoing experiments indicate that potassium penetrates the cellular membrane freely. 5. Chloride ion acts in a manner eniirely comparable to potassium. G In addition to the electrical effects discussed above, the two compartments of a simple Donnan system will generally be at different pressures. At equilibrium, the compartment containing tile nondiffusing ion (protein) will contain the greater number of particles. Such an osmotic imbalance results in a shift of water to tlle protein-containing compartment. This water shift and subsequent rise in pressure within tile protein (intracellular) compartment may be avoided by adding sufficient nondiffusing solute to the protein-free (extracellular) compartment. Tile concentration of sodium ion in tile extracelhdar space is sufficient to produce isosmolarity with the intracellular compartment. However, this ion has been shown to play a far more dynamic role than that of a passive, impermeable solute. It has been found that although tile cell membrane is some 30 times less permeable to sodium titan to potassium ion, the former passes across the membrane in considerable numbers, r Hence the resting cell membrane cannot be thought to be impermeable to sodium. Reference to equation 2 reveals that by its concentration ratio alone, the low intracellular and high extracellular concentrations of sodium might be thought to produce a potential whose polarity is tile opposite of that observed. There is only one way to reconcile this paradox in view of the appreciable permeability of tile membrane to sodium: the inward flux (F1) of sodium ion must be 50 to 100 times that of the outward flux (F~). Radiotracer studies, however, have revealed a ratio many times smaller.~ Indeed, these studies confirm the fact that the intact resting cell must be in sodium balance. If it is presumed that the inward flux of sodium is an ionic one, but that an equivalent amount of sodium is "sneaked" across ttle membrane in complex form, the ioliic flux ratio would agree with the predicted ratio. The exact manner in which sodium might be expelled from a cell is not known. Terms such as "active transport" and "sodium pump" lmve been used to describe the process. A theoretical sclieme outlined by one group of investigators s is presented in figure 6. Here an intracellular substance "P" combines with intracellular sodium ion and the combination passes across the membrane in complexed form. In the extracellular compartment, dissociation of tlle P N a + cbmbination is much favored by tile great affinity of ground substance (GS) f o r P . Sodium ion is thereby free to rediffuse into the cell. The other constituefits ot~ the extra- and intracellular compartments are distributed in accord \vith the-potefitial developed by the active transport or pumping of sodium arid the Donnan equilibrium. On the basis of its physical and chemical properties and its distribution in tissue, histamine has been proposed as being a likely "pump substance. "D It might be added that serotonin is at least as likely a candidate. Whatever the mechanism responsible for the extrusion of intracellular sodium ion, it appears that metabolic energy is introduced at this point. Whether it is ex-
213
IONIC EXCtIANGES AND CARDLa.CACTION POTENTIAL
CL-
c4J'el.-
PROTEIN-
NA.P Gs pG S ÷
K+
l~t÷
[K+ K÷
FIG. 6.--Equilibria across resting cell membrane (rectangle). P is pump substance,..GS is extracellular ground substance. Dashed arrow represents flux of sodium in complexed form. (After Briller, S. A.: Ionic basis of the transmembrane potential. In Kossman, C., Ed.: Advances in Electrocardiography. New York, Grune & Stratton, 1958.)
pended in the synthesis of a "pump substance" or in some other modality is a matter of much speculation. Tile sodium pump, in summary, can be viewed (1) as a dynamic osmoregulator which prevents the accumulation of intracellular sodium and water and (2) as a Donnan mechanism complement .with which rapid adjustment of the transmembrane potential can be made in response to activity and stress. Activity of the sodium pump would appear to account for the following facts: (1) significant changes in the resting potential of nerve cells are not obtained after the microinjection of potassium in amounts sufficient to produce a calculated change of about 33 per cent lo., (2) the natnre of the electrodes used to measure the resting potential appears to have..little effect on tile magnitude of the voltage detected. If a Donnan equilibrium were the sole source of the resting potential, no voltage should be detectable with the unmodified silver-silver chloride electfodes used in this w°rkl°; (3) the internal/external potassium ratio differs significantly from the external/internal chloride ratio although these ratios'should be identical according to classical Donnan theory. 1° .... It is of interest that there may be an alternative explanation for the'lastcited observation. StSmpfli has recently shown that potassium perm'eabi.lity of nerve may be dependent upon the magnitude . . . . of the restingp6[ential. 11=~,. . When the latter is large the potassium permeabdlty is suddenly and ~significantly reduced. It is implied that the resting potehtial of intact tissue 'i~ dependent chiefly upon the transmembrane chloride ratio. Under t h e s e con'-¢: ditions variation of the extracellular potassium ratio would have little effect upon the resting potential. However, even minimal trauma t ° the tissue under study may reduce the resting potential sufficiently to augment potassium permeability a n d in effect switch on the potassium '¢battery."
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STANLEY A. BRILLER
TIIE ACTIVEBIOLOGICSTATE Maintenance of the resting potential of a cell has been shown to represent a manifestation of the expenditure of metabolic energy in bringing about a unique separation of the monovalent ionic constituents of the cell. The active state will be seen to demonstrate the results of allowing this separation to lapse in a carefully integrated manner. Hodgkin, Huxley and Katz ~-° demonstrated that the greater impermeability of the resting membrane of an axon to sodium can be abruptly abolished by reducing the resting potential electrically. Such a reduction in potential may be brought about by a natural or artificial pacemaker or by currents from adjacent active cells. The effect of allowing freer flux of sodium ion across the cell membrane (which maintains its resting semipermeability to potassium) is that the sodium pump mechanism becomes overwhelmed. Consequently there is relatively free movement of sodium ions in both directions across the membrane although inward movement of this ion predominates. ~ Unrestrained sodium movement impelled by its concentration gradient is therefore able to deliver free energy to the cell in the form of electrical potential which tends to make the inside of the cell less negative. Such a change in potential in turn makes the membrane more permeable to sodium and, coupled with the presumed inactivation of the sodium pump mechanism, the intracelhdar potential rises past zero toward the level p r e d i c t e d b y equation 1 for sodium ion. r It should be noted that during this process the cell gains a number of sodium ions. However, the net gain is but an infinitely small proportion of the sodium already there23 As the movements of sodium ions across the membrane reach a peak (at which time the intracellular potential is positive in polarity) the membrane gradually begins to increase in permeability to potassium. These latter ions, impelled by the hostile positively charged intracellular environment, leave the cell in numbers greater than the number of entering potassium ions. These free movements of potassium (coupled with the now decreasing permeability of the membrane to sodium) reduce the positive potential within the cell. Finally, as the impermeability of the membrane to sodium is completely re-established, potassium equilil)rium potential dominates once again and the intracellular potential resumes its negative polarity. During the later phases of the "active state," the potassium permeability gradually declines to its previous level. Such changes in sodium and potassium permeability and intracellular potential for a nerve celP 4 are shown in figure 7. It will be recalled that the cell has gained sodium and lost potassium in passing through the active state. Reactivation of the sodium pump with subsequent extrusion of sodium coupled with re-entry of potassium occurs promptly 1~ and is synchronous with ~;arying degrees of nonresponsiveness of the cellular mechanism known as the absolute and relative refractory periods. The large size of certain axons, the simplicity of their geometric form and, most of all, the ability of a nerve cell to pass through its active phase without moving have made it possible to document the foregoing ionic behavior of
215
I O N I C E X C I I A N G E S A N D CARDIAC A C T I O N P O T E N T I A L
90
35-
F
P
30-
70
25 50
40
-
20 _-:-
-
3020lo;ok
x
g
T 3
o msec.
I 35
t 4--"
"----
Fie. 7.--Calculated action potential V and ionic eonductances (gK potassium, g.~a sodium, g total condnctance) of a propagated nerve impulse. (From ttodgkin, A. L., and Huxley, A. F.: A quantitative description of membrane current and its application to conduction and excitation in nerve. J.Physiol. 117:500, 1952.) this tissue with precision. Repetition of similar direct studies in a single myocardial fiber has been impossible thus far. Although there is little reason to snspect that there are basic differences in tile generation of the resting potential in a myocardial fiber and in nerve, there are unique features of the active myocardial process: (1) Except for similar speed and magnitude of tile upstroke, tile morphologies of action potentials of myocardial (fig. 8) and nerve cells (fig. 7) differ vastly. The total duration of the action potential of a myocardial cell may be several hundred times that of a nerve cell. (2) Although the time variation of the total membrane condnctance of an active nerve is a fairly smooth monophasie curve (fig. 7), 1~ a plot of the same parameter in a kid Purkinje fiber (fig. 8) 16 is triphasic. These observations suggest that depolarization in laeart muscle and in nerve is due to similar mechanisms: a regenerative relationship between (a) reduction in resting potential by adjacent cells, (b) increases in membrane permeability to sodium and (c) net entry of this ion into tile fiber. Presumed decline of active transport a n d hyperpermeability of ionic sodium (documented by a synchronous increase in membrane conductivity) permit the peak of tile action potential to approach the positive equilibrium voltage predicted by equation 1 for the transmembrane concentrations of sodium. Although the action potential falls fairly rapidly at first (phase I), it hovers about zero potential for several hundred milliseconds (phase II) at a time when the total membrane conductance abruptly decreases. These values of potential and total membrane conductance can be explained o n l y by a decline in potassium conductance which greatly exceeds a simultaneous diminution in sodium conductance, lr Since the intracellular potential at this time can be expected to force potassium out of the cell, a decline ih potassium conductance would serve to minimize loss of this ion to the extracellular space. Indirect confirmation of this premise has been obtained by Conn and Wood, who found that in the isolated, perfused dog heart, tile
216
A. BRILLER
STANLEY
o II
I
| 5, I
H
,mV
!
I I
2o
I I I
o
gtotal
-2( -.0
-4( -6C -8C
II
9.01
I
I
I
I
I
I
0.5 S E C O N D
I
I
I
I
901
I
Fic. 8.--Action potential (with phases I, II and III of repolarization identified between vertical dashed lines) of kid Purkinje fiber. Simultaneous values of total membrane conductance (gtotal) in relative units. Conductance values calculated from membrane resistance measurements of \VeidmannJ c (Adapted from Weidmann, S.: Resting and action potentials of cardiac muscle. Ann. New York Acad.Sc. 65:663, 1957.) exchange rate of potassium was one-half that of sodium, is The pulsatile nature of the potassium efltux in the turtle heart has been noted by others1? and may be greatest during phase III of repolarization when the total membrane conductance increases to near-diastolic levels. Since artificial enrichment of extracellular potassium is known to shorten the duration of the action potential of heart muscle, the natural extracellular accumulation of this ion as a result of depolarization is believed to initiate the repolarization process. 16 Active extrusion of the previously accumulated sodium coupled with the re-entry of lesser amounts of potassium would then serve to complete the cycle. There is the possibility that these latter events begin during phase III of repolarization. As applied to electrocardiography in a qualitative sense, the QRS deflections take origin from free, transmembrane movements of sodium ions whereas the T wave is probably ascribable to comparable activity of potassium.
IONIC F~XCIIANGESAND CARDIACACTION POTENTIAL
~0~7
The crux of the mechanism of tim action potential is the ability of the cell membrane to undergo tile required serial, selective changes in permeability to sodium and potassium ions. Although calicum ion, a most necessary ingredient for nerve and muscle function, apparently plays no direct role in generating the transmembrane potential, it is believed to be active in regulating membrane permeability, s Wilson and Nachmansohn 2° believe that acetylcholine is implicated in causing alterations in the molecular structure of the membrane during activity. Others 7 indicate that the amount of heat generated during activity is too small to suggest an origin other than that due to movement of ions through the membrane. A functional, submicroscopic view of the biologic membrane theoretically would reveal (a) pores through which ions pass and (b) intervening, totally impermeable areas of membrane substance. The electrical analogs of (a) and (b) are a resistance and a capacitor, respectively. Studies of the alterations in cell membrane impedance during the action potential have shown that the capacitance of the membrane is constant. -°~ These observations strengthen the contention that changes in membrane permeability do not imply structural alterations, and direct attention to the pore moiety. In this light, studies of artificial membranes carrying fixed charges presumably on their pore walls are of considerable interest. Sollner et al. have shown that such membranes may discriminate between sodium and potassium ions. ~°z Only future work can determine whether such charged pores exist within biologic membranes and; moreover, whether these charges are time-dependent fimctions of the membrane voltage as required by the Hodgkin-Huxley thesis. ~4 The latter theory is an elegant mathematical expression of the relationship between the action potential and the various ionic currents of a squid axon; the ideas expressed in it underlie much of tim discussion of the active biologic state in this article. REFERENCES 1. Leaf, A.: Maintenance of concentration during nervous activity. J.Physioh gradients and regulation of cell vol114:119, 1951. ume. Ann. New York Acad.Sc. 72: 6. Ussing, H. H.: Ion transport across 396, 1959. biological membranes. In Clarke, H. 2. Donnan, F. G.: Theorie der MembranT., Ed.: Ion Transport Across Memgleichgewichte und Membranpotenbranes. New York, Academic Press, tiale bei Vorhandenseln von Nicht 1954, p. 3. Dialysierenden Elektrolyten. Ein 7. Hodgkln, A. L.: The ionic basis of elecBeitrag zur Physikalisch-Chemiscben trical activity in nerve and muscle. Physiologic. Zeitschrift Fur ElcktroBiol.Rev. 26:339, 1951. chcmle 17:572, 1911. 8. Parlin, R. B.: Membrane permeability 3. Boyle, P. J., and Conway, E. J.: Potasand electrical potcntial.. In Clarke, sium accumulation in muscle and H. T., Ed.: .Ion Transport Across associated changes. J.Physiol. 100:1, Membranes. New York, Academic 1941. Press, 1954, p. 103. 4. Conway, E. J.: Nature and significance 9. Eyring, H., and Dougherty, T. F.: of concentration relations of potasMolecular mechanisms in inflammasium and sodium ions in skeletal tion and stress. Am. Scientist 43:457, muscle. Physiol.Rev. 37:84, 1957. 1955. 5. Keynes, R. D.: The ionic movements 10. Grundfest, H.: The nature of the elec-
218
11. 12.
13.
14.
15.
16.
17.
STANLEY A. BRILLER trochcmical potential of bioclectrie tissue. In Shedlovsky, T., Ed.: Electrocbemistry in Biology and Medicine. New York, John Wiley & Sons, 1955, p. 141. Sffimpfli, R.: Personal communication. Hodgkin, A. L., Huxley, A. F., and Katz, B.: Measurement of current voltage relations in the membrane of tim giant axon of Loligo. J.Physiol. 116.'424, 1952. Keynes, R. D., and Lewis, P. R.: The sodium and potassium content of cephalopod nerve fibers. J.Physiol. 114:151, 1951. Hodgkin, A. L., and Huxley, A. F.: A quantitative description of membrane current and its application to conduction and excitation in nerve. J.Physiol. 117:500, 1952. - - , and Keynes, R. D.: Active transport of cations in giant axons from Sepia and Loligo. J.Physiol. 128:28, 1955. Weidmann, S.: Resting and action potentials of cardiac muscle. Ann. New York Acad.Sc. 65:663, 1957. Brady, A. J., .and Woodbury, J. W.: Effects of sodium and potassium on
18.
19.
20.
21.
22.
repolarization in frog ventricular fibers. Ann. New York Acad.Sc. 65: 687, 1957. Conn, H. L., and Wood, J. C.: Cation exchanges in tlle heart: relation to tile cardiac action potential. J.Clin. Invest. 37:885, 1958. Wilde, W. S.: Tile pulsatile nature of the release of potassium from heart muscle during the systole. Ann. New York Acad.Se. 65:693, 1957. Wilson, I. B., and Nachmansohn, D.: Tile generation of bioelectrie potentials. In Clarke, H. T., Ed.: Ion Transport Across Membranes. New York, Academic Press, 1954, p. 35. Cole, K. S., and Curtis, H. J.: Electric impedance of the squid giant axon during activity. J.Gen.Physiol. 22: 671, 1939. Sollner, K., Dray, S., Grim, E., and Neihof, R.: Membranes of high electrochemical activities in studies of biological interest. In Shedlovsky, T., Ed.: Electrochemistry in Biology and Medicine. New York, Jolm Wiley & Sons, 1955, p. 65.