SPECIAL ARTICLE
The Electrical Potential Difference Across
the Cell Membrane of Heart Muscle
Biophysical Considerations
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By ERNEST PAGE, M.D.
T HE CELL MEMBRANE of mammalian
heart muscle cells may be characterized
by three interrelated observations. In the first
place, the membrane separates an intracellular
solution having a high potassium (K) and a
low sodium (Na) concentration from an extracellular solution with a high Na and low
K concentration. Secondly, K and Na ions
can be shown with radioactive tracer technics
to be continuously passing into and out of the
cell; to do so, these ions. must cross the cell
membrane, which is therefore said to be permneable to them. In spite of the apparent permeability of the membrane to both Na and K,
the intracellular concentrations of these ions
are observed to remain remarkably constant.
Finally, an electrical potential difference of
80 to 90 millivolts can be measured across the
cell membrane of quiescent (noncontracting)
heart muscle cells between an electrode in the
intra.cellular solution and a sinmilar electrode
in the solution bathinlg the exterior of the
cell. This electrical potential difference cannot be detected by measurenments from the
outside of intact cells as in the electrocardiogram. It may, however, be observed either as
the "injury potential" of cells with damaged
cell membranes or as the somewhat larger
"resting potential" in cells whose cell membrane has been pierced with a microelectrode.
The sign of the electrical potential difference
across the cell mnembrane undergoes periodic
reversals called "action potentials." The
time course of the vectorial summation of
such action potentials fromn many cells is reflected in the QRST complexes of the surface
electrogram and conventional electrocardiogram.
Theory
The study of the electrical potential difference across ion-permeable membranes separating two salt solutions of different ionic
composition is a province of physics and of
physical chemistry, which attempt to formulate in mathematical terms an exact and rigorous description of the processes involved.1' 2
The present article explains the same physical
and physicochemical processes in nontechnical language in order to promote a better
understanding of cell-membrane phenomena
among clinical cardiac physiologists.
Since many aspects of the behavior of cell
membranes cani be reproduced experimentally
with artificial membranes,3-6 it is useful to
begin bv inquiring how electrical potential
differences may arise across such artificial
membranes. To take an apparently simple
model, consider two well-stirred reservoirs of
equal and fixed volume separated by a porous
partition or membrane (fig. la). Let the left
reservoir be filled with a solution of potassiuni
chloride (KCI) at a conceentration of 200 millimoles per liter and the right reservoir with
a KCI solution at a concentration of 5 millimoles per liter. Assume that movements of
From the Biophysical Laboratory, Harvard Medical
School, Boston, Massachusetts.
582
Circulation, Volume XXVI, October 1962
ELECTRICAL POTENTIAL DITFFERENCE
583
lb.
la.
i d.
Ic.
I
KCI 200 mM
I
0
KCI
I
0
5mM
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NO POTENTIAL
DIFFERENCE
DIFFUSION
POTENTIAL
MEMBRANE LESS
MEMBRANE
PERMEABLE
EQUALLY PERMEABLE
TO Cl- THAN TO K+
TO Ci- AND K+
MAXI MAL
POTENTIAL
DIFFERENCE
MEMBRANE
IMPERMEABLE
TO Cl-
rigure 1
The electrical potential difference produced during diffusion of
a model membrane.
wa.ter through the porous partit,ion are prevented. Only KCl can then move through the
membrane. When diss,olved in water, this salt
separates into two particles of equal and opposit.e charge, the K and Cl ions. Each ion
surrounds itself with a number of molecules
of the solvent, water (the so-called hydration
shell), and henceforth behaves as an independent molecule, an important restriction
being that for the solution as a whole or any
microscopic portion of it the sum of the K
ions be, always, equal to the sum of the Cl ions.
The unequal partition of dissolved KCI on
the two sides of the membrane will give rise
to a, redistribution of the dissolved salt by a
random process called diffusion. Since the
concentration of KCl in the left reservoir is
initially 40 times as great as that in the right
reservoir, there will initially be 40 times as
great a tendency for KCI to diffuse from left
to right as from right to left. As a consequence, a net movement of KCl from left to
right is set up. This net movement will continue until the concentrations in the two
reservoirs have become equal, i.e., until the
gradient of concentration has been abolished
by the trans.fer of KCI from left to right. If
Circulation, Volume XXVI, October 1962
a
KCl solution
across
the positively charged K ions and the negatively charged Cl ions move through the membrane with equal ea-se, the membrane is said
to be, equally permeable to K and Cl. These
positively and negatively charged particles
will then pass t.ogether through the pores in
the membrane, electrically neutralizing each
other. The net movement of KCI will occur
without a separation of positive from negative
charge, and a device for measuring the electrical potential difference across the membrane will accordingly register zero volts while
the diffusion is in progress (fig. lb).
Suppose, now, the membrane is altered so
that the passage of the Cl ion across the membrane is made more difficult than that of the
K ion. Then, as K and Cl move from left to
right under the force set up by the gradient
of concentration, a thin cross-section of the
membrane will show the advancing front of
the net diffusion process to consist of the
readily penetrating, positively charged K ions.
These K ions will drag behind them by the
force of electrostatic attraction the negatively
charged Cl ions whose movement is impeded
by the membrane (fig. ie). KCI now diffuses
as a dipole, oriented so that the positive pole
PAGE
584
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(the K ion) is leading and the negative pole
(the Cl ion) is following. A sufficiently sensitive voltmeter across the thin section of the
memnbrane will indicate that the right face of
the membrane is electrieally positive with
respect to the left face. The reading oni the
voltmeter reflects a separation of positive
fromn ilegative charges such that the positively
charrged K ions are at a relatively higher concentration toward the right face of the membrane and the negatively charged Cl ions are
more concentrated toward the left face. An
electrical potential differenee arising in this
way is called a diffusion potential. It stems
from the difference iii the mobility within
the membrane pores of the positive anid
negative ions of a salt diffusing through
the memnbrane. The spatial separation produced by the membrane between the K amid
Cl ions need be very slight, a separation
of a small fraction of an Angstromn unit
inivolving only a small number of KCI
nolecules sufficing to gemierate a very appreciable potential difference. [One Angstronm
unit (abbreviated A - 10-1i nmeters = one
ten billionth of a mueter.] A diffusion potential
exists while an actual net moveunelit of EC1
through the miieinbrane is unider way. The
existence of a diffusion potential and the fact
that its magnitude cail be shown to depend
on the coneentration of a given ion are therefore evidenee that the mnembrane is permneable
to that particular ion.
In the interaction betweeni menmbranes and
salts like KCI there is a continuous gradation
in the degree to which the membra.ne restricts
the nlovements of either positively charged
ions (cations) or negatively charged ions
(anions). At the onie extreme, the membrane
brings about no separa.tion of positive froni
imegative charge and no diffusion potential
(fig. lb); the mobilities of cation and anioli
in the membrane are equal. At the other extreme, the memnbrane is permeable only to ions
of one charge (e.g., to the cation, K) and
totally impermeable to ions of the opposite
charge (e.g., to the anion, Cl). The separatiom
of charge and hemmee the electrical potential
difference produced are maximal (fig. ld).
Intermediate between these two extremes is
the type of diffusion potential (fig. lc) that
corresponds to the situation at many eell membranes (See Appendix 1).
The three cases are summarized mathematically
by the Nernst Equation. For the diffusion of a
potassiuml salt at 370 C this equation takes the
form
vm
([K] [K]0)
61.5log
=- U
u-I- uin which Vm is the electrical potential difference
across the mnembrane, u+ and u- are the mobilities
(velocities per unit force) of K and Cl within
the membrane, and [K] i and [K]. are the concentrations of K in the solutions on either side
of the membrane (the "inside" and "outside" solutions, respectively). When the electroheemical mlobilities of cation and anion are equal (u+ - u-), the
fraction cointaining the mobility termns vanishes
and Vm = 0. When the anion mnobility in the
mnembrane, u-, is zero (the imlemibrane is impermeable to Cl), the u's cancel and Vm becomes equal
to -61.5 log (L[K]I/[K0). Under these conditions Vm depends only on the ratio of the K
concentrations in the solutions bathing the two
sides of the membrane. Finally, if us and u- are
unequal and neither is zero, Vm is the type of
diffusion potential believed to exist across heart
nusele cell membrane (See Appendix 2).
It is pertinent to consider next by what
mechanismts a porous mnembrane niay impede
the diffusion of one ion of salt like KCl so as
to bring about a separation of positive from
negative charges and, hence, to set up a diffusion potential. Diffusion of ions through
the membrane probably occurs via the waterfilled pores in the mnembrane. A membrane
may therefore be expected to impede the
transit of ions of a size large compared to
the diameter of its pores, while permitting the
movement of ions whose diameter is relatively
small. Figure 2 compares the hydrated ion
diameters (the diameter of the ion plus the
shell of water molecules that moves with it)
of K, Na, and Cl with the diameter of the
pores in the cell membrane of eat ventricular
muscle. These pores have recently been shown
to have a diameter not in excess o;f 8A.7 It
will be seen from figure 2 that the membrane
inight be expected on the basis of relative ion
size to be more permeable to K and Cl ions
Circulation, Volume XXVI, October 1962
585
ELECTRICAL POTENTIAL DIFFERENCE
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than to the larger Na ion. The diameters of
the K and Cl ions, however, are sufficiently
similar that the pores of the membrane cannot
discriminate between them by virtue of their
size. Since such discrimination is required in
order to generate a diffusion potential, it is
necessary to look for an additional mechanism
for separatnig the positively charged K ion
from itis negatively charged ion partner.
In figure 3 a simplified model of a membrane pore is depicted as lined with fixed
negative electrical charges, that is, with negatively charged molecules built into the substance of the walls of the pore. These fixed
charges attract, by the force of electrostatic
at-traction, ions having an electrical charge
opposite to their own charge, and repel, by
the force of electrostatic repulsioni, ions having the same charge as their own. The sites
at which the fixed charge groups abut oni the
water-filled lumen of the pore become coated
with oppositely charged ions from the solutioln, the counter-ions. Unlike the fixed
charges themselves, counter-ions are free to
exchange with other K ions in the solution.
If the pore is wide enough (fig. 3a), the electrostatic effects of the fixed charges do not
appreciably influence the diffusion of ions
through the membrane. As the pore becomes
progressively narrower, however, the fixed
charges become increasingly effective in exeluding ions of like sign (fig. 3b). At a certain critical pore diameter, only ions of opposite sign, in this case, K ions, can pass (fig.
3e). The existence of fixed charges in cell
membranes is strongly suggested by their
selective permeability to ions and by the finding that, isolated membrane fragments contain
lipid-c arbohydrate-protein complexes with
electrically charged lipid components.8
The nature of a diffusLion potential has been
discussed with reference to the two-compartment. model of figure la in which a porous
membrane separates a 200 mM KCl solution
from a 5 mM KCl solution. It is apparent
that with the passage of time the model will
tend to run down, i.e., when both K and Cl
can -permeate, the diffusion will come to an
Circulation, Volume XXVI, October 1962
DIAMETER OF PORES
OF CAT HEART
MUSCLE CELL MEMBRANE:
8.0 A OR LESS.
ION
(
A
DIAMETER
0
A
Na
5.12
K
3.96
CI
3.86
H20
1.5
0
NOT
( IONIZED J
Figure 2
Comparison of size of ions and water with pore
size of cat heart muscle cell membrane.7' 34, 35 *Ion
diameters include the hydration shell of the ion.
end as the concentrations of KCl on the two
sides of the nmembrane approa.ch equality.
What is required for a maintained diffusion
alnd therefore for a. maintainted diffusion potential is a mechanism that continually replenishes the KCl coneentration in the 200
nM reservoir and continually depletes the
KCI cloneentration in the 5 mM reservoir. The
rates of repletion and depletion must be sufficient to keep up with the rate at which KCl
diffuses from left to right, down the concentration gradient, through the pores in the
membrane. Sueh a mechanism would set up
a steady state in which, by some energy-consuming process, KCl is transported "uphill"
against the concentration gradient from the
5 mM compartment into the 200 mM compartment as fast as it is lost from the 200 mM
compartment by diffusion "downhill."
The situation is analogous to that of two
lakes with different water levels separated by
a leaky dam. For the purposes of this analogy,
the difference in water levels is maintained
by pumping water from the lower lake into
the upper at a rate equal to that at which
PAGE
586
KCI
200 m M
(39
(D( (3 (3
(D E (±- (D (
(3 (3 (D (3
(3 @30303
0000F
KCI
5
mM
(D (3 (D se
Wide
pore.
K+ and Cl-pass readily.
No potential difference.
Intermediate pore.
Cl- partially excluded.
Diffusion potential.
Narrow pore.
Cl- totally excluded.
Maximum potential difference.
b.
C.
Figure 3
Effect of fixed charges onz permea-bility of membrane to ions. The schematically indicated pores are shown as lined with fixed negatite electrical chalrges. KCO is diffusing
from the 200 mM solution on the left into the 5 mM solution on the right. Modified
0.
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after Sollner.3
water leaks through the damti froimi the upper
into the lower lake. The same pumping meehanism that miiailitains the difference of water
levels also perpetuates the leak.
The cell membranie of heart mnuscle, in common with that of virtually all living cells,9
is the site of energy-consuming mechanismis
for mnoving ions and other molecules against
concentration and electrical gradients. These
tuphill" processes, ofteni referred to as "active transport," derive their energy supply
from cellular metabolic reactions, most probably fromn the terminal high-enlergy phosphate
bonid of adenosine triphosphate. By contrast,
the "downhill" diffusion, which the "uphill"
processes serve to maintain, oceurs spontaneously without the necessity for a special
metabolie energy input, and such "downhill"
diffusion is consequenitly termed "passive
transport " (See Appendix 3). Unlike downhill" diffusion, active transport does not occur
through water-filled pores in the membrane.
Instead, for the purpose of transport against
concentration and electrical gradients, K and
Na appear to combine at the inembrane surface with certain molecules called carriers or,
colloquially, "ion pumps," which are part of
the substance (matrix) of the membrane itself. In heart muscle this conibination, usually
r eferred to as anl ion-carrier complex, will
have to remain hvpothetical umntil it is chem"
ically i(lenL-tified. In tissues in which such ioncarrier complexes have been more closelv
studied, 11 they displav mnany of the characteristies of enzyvmes.
Experimental Approaches'
The theoretical considerations presented so
far suggest that the ion permeability of heart
muscle-cell menubrane should be accessible to
measurement bv three experimeental approaches. These include the measurement of
intracellular ion colncentrations and cell volumes, of the electrical poten-tial differenee
across the cell membrane, and of the rate at
which radioactively labeled ionis pass through
the inembrane into and out of the cell.
Figure 4a shows the intracellular K anid Na
concentrations in papillary mLuscles from the
right ventricles of cat hearts, 12 iimmersed in
a solution having the approximnate K and Na
concentration of cat plasma. It is, apparetit
from the figure that the cell membrane is the
site of a steep cooncentrationi gradient of 200
mM to 5.3 mM favoring the diffusion of K out
of the cell, and an almost equally steep concentration gradient of 178 muM to 5 mnM favorinig the diffusion of Na into the cell. Now
assume that the ainion, Cl, will passively aecompany any outward diffusioni of K or inward diffusion of Na. Then-, in terms of the
mlodel previously developed, the concentration
gradients for K anid Na produce a curious
Circulation, Volume XXVI, October 1962
EliECTRICAL POTENTIAL DIFFERENCE
51-87
b.
INTRACELLULAR
K200
Na
5
EXTRACELLULAR
No
178
K
5.3
INTRACELLULAR
EXTRACELLULAR
F
FK
LL
200 mM|
N c 5 mM|
Na 178 mM|
\
5.3m
K5. M
i
Figure 4
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(a) Intracellular and extracellular K and Na concentrations in resting cat papillary
muscle.7 12 (b) Steady state model corresponding to (a). K and Na diffuse "downhill"
through the pores in the membrane in the direction indicated by the solid arrows;
they are returned "uphill" by arn active transport mechanism located within the
substance of the membrane.
situation (fig. 4b), with the possibility of two
oppositely directed diffusion processes setting
up diffusion potentials of opposite algebraic
sign. The electrical potential difference actually measured a,cros,s the cell membrane will
represent a summation of these two opp,osite
diffusion potentials. Since only ions that can
diffuse through the membrane can be effective
in producing a diffusion potential, the relative contributions of K and Na to the electrical potential difference in heart muscle
depend on the relative permeability of the
cell membrane to these two cations (See Appendix 4).
Figure 5 illustrates an experimental method
for comparing the K and Na permeabilities
of the cell membrane of quiescent cat papillary muscle.7 12 The experimental procedure
was, to raise the K concentration of the solution ba,thing the external surface of the cell
membrane a,pproximately 10-fold by a molefor-nmole substitution of K for Na, keeping
the total concentration (K + Na) constant.
After a period of equilibration sufficiently
long for completion of all net movements of
ions and water, the ecell volumes and intracellular ion concentra,tions, of the muscle were
determine,d. When K was substituted for Na
in this way, the cells behaved as, if they had
been placed in a hypotonic solution, i.e., they
took up water and swelled. Chemical analysis
of the muscle revealed the intracellular K
Circulation, Volume XXVI, October 1962
concentra,tion to be unchanged, while the
cellular water and K content ha,d increased.
The cellular uptake of K, Cl, and water shows
that the cells, are permeable to these three
molecules. Looked at in another way,, the
experiment demonstrates that resting heart
muscle is normally sufficiently impermeable
to the Na ion for the extracellular Na to behave osmotically like an impermeant substance. Thus, when the external Na coneentration is lowered to 133 mM, the deficit in
tonicity cannot be made up by an equivalent
concentration of K, since K, unlike Na, is an
ion to, which the cell membrane is readily
permeable.
As previously stated, those ions to which the
cell membrane is, most permeable will contribute most significantly to the observed electrical
potential difference a-cross the membrane.
Figure 6 illustrates the dependence of the
electrical potential difference across the cell
membrane of quiescent ca,t papillary muscle
on the concent-ration of external K13, shown
by the experiments just described to be a relatively permenant cation. In figure 6, the full
line is the value the potential difference should
have if it, depended only on the ratio of the
intracellular and extracellular K concentrations according to the relation, Vm = -59.6
log( [K] i/ [K] o). The broken line connecting
the experimental points indicates. the ele.ctrical potential difference actually measured
PAGE
588
NORMAL EXTERNAL
K CONCENTRATION
IOX NORMAL EXTERNAL
K CONCENTRATION
(SUBSTITUTE K FOR NO)
150_
E
z
u
*_
_
o
fL_
[K]1 = 200 mM
CI
50 _
I
1
2
3
5
10
EXTERNAL K CONC
[K]0
[No]
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[K]0+ [Na]o
=
5 mM
[K]o
=
50 mM
=
178 mM
[Na]o
=
133 mM
=
183 mm
=
183 mM
[K]0+ [No]o
Figure 5
of permeability of cat p,apillary
Comparison
munscle cell membrane to K and Na.7 Left: Cell
volume acnd intracellular K concentration in solution with normal external K concentration; rigbt:
in solution with 1OX normal external K concenmole for mole substitution of
tration, made by
K for external Na. Increase in cell volume exaggerated for illustrative purposes.
a
with the intracellular microelectrode technic.
In this techn-iie a glass electrode with a tip of
less than 0.5 muieron is introduced into the
cell; the hole so nmade in the cell memnbrane
is, well sealed and small enough so that there
is no significant admixture of intracellular
and extracellular solutions. The observed potential differenee is large at physiological (5.3
mM) and lower external K colncentrations; it
dinminishes progressively as the external K
concentration is raised, i.e., as the difference
in K coneentrations on the two sides of the
membrane beeomnes smaller. At the higher
external K concentrationis the slope of the
broken line approaches that of the theoretical
line; at physiological anid lower external K
conceltratiomis the experimental slope is much
less steep tha.n the theoretical, and the observed electrical potential differen-ce is progressively less than that predicted from the
ratio of the intracellular and extracellular K
concentrations. These phenonmena are conveniently iliterpreted in terms of the twocompartment mnodel of figure 4b, which repre-
20
30
50
iGS
(mM)
Figure 6
D)ependen cc of electrical potential difference across
the cell membrane of quiescent cat papillary
muscle on external K concentration.3 The intracellular K concentration is constant at 200 mM.
Experimental points connected by brok-en line
are the ralues of the electrical potential difference
obtained with the intracellular microelectrode
technic. The solid line is the value the electrical
potential difference would have, if it depended
exclusively on the ra'tio o f intracellular to extracellular K concentrations according to the relation Vr,n = -59.6 log ([K]i1/[K] j (temperature 27.5' C).
sents a sumiationi of two oppositely directed
diff-usioni processes setting up a potential difference whose magnitude depends on the relative permneabilities to K and Na. The experimnental observation is that at low external K
con-centrations the electrical potential differeicce across the nmembrane does not depend
solely on the outward diffusion of K. The
membrane permneability to Na in the resting
steady state, though small relative to that for
K, is sufficienitly important that the inward
diffusion of NaCI contributes significantly to
the potential difference.
A third method for characterizing the cell
mnemubrane is the nmeasureient of the rates of
movenment of ions aeross the membrane by
use of radioactive tracer technies.14 The rate
of movement of an ionI across a membrane is
referred to as an ion flux; such a flux mnight
be expressed, for example, as picomoles of K
crossing unit area of cell inembrane per unit
tinme (pmnol/em2 mini). (One picomole - 10-12
mole -one millionth nmillionth mole.) A subCirculation, Volume XXVI, October 1962
ELECTRICAL POTENTIAL DIFFERENCE
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stance to which the membralne is permeable
is continuously pass,ing through it in both directions. Accordingly, the ion movement may
be considered as made up of two components,
one directed into the cell, called the influx,
and one directed outward, called the outflux.
The net flux, repres,enting the difference between influx and outflux, determines whether
the cell is gaining or los,ing the substance being traced. The net flux is zero in the steady
state, an important special case in which the
influx and outflux are equal, i.e., in which the
rate of cellular accumulation equals the rate
of loss. This condition, which prevails in the
quiescent heart muscle cell, is necessary if the
intracellular ion concentrations and the related electrical potential difference are to remain c.onstant. In terms of the model of figure
4b, the Na, influx occurs "downhill" with respect to electrical aand concentration gradients; it must therefore in the steady state be
equal to the Na outflux a,gainst the electrochemical gradient, and, similarly, the "downhill" K outflux must be balanced by an equal
and opposite "uphill" K influx.
As indicated in figure 4b, the "downhill"
fluxes of Na and K probably occur through
water-filled pores in the membrane. Accordingly, these "downhill" movements may be
expected to obey in a gene.ral way the physicoehemical laws applicable to electrolytes, in
aqueous solutions.15 16 The "uphill" fluxes,
on the other hand, appear to involve surfa.ce
reactions with the substance of the membrane
and obey a different set of physicochemical
laws applicable to such surfa,ces. Consequently, the criterion of whether a particular ion
flux obeys the phys,icochemical laws of aqueous solutions or of reactions a,t surfaces is
useful in identifying the flux as passive or
ae.tive.17' 18 A detailed consideration of this
and other criteria of a.ctive and passive transport, as well as of the carrier hypothesis of
active transport, is, beyond the scope of this
article. It is, however, instructive to point out
certain other characteristics, of the energyconsuming "uphill" fluxes. An inadequate
oxygen supply, inhibition of respiration with
Circulation, Volume XXVI, October 1962
589
carbon monoxide or cyanide, failure to supply
a substrate to act as a "metabolic fuel," or
the uncoupling of oxidation from phosphorylation with dinitrophenol, all inhibit active
transport by depriving it of its energy supply.
Similarly, the cardiac glycosides appear to
interfere with active transport, possibly by
competing with the ion transported for the
site of combination with the carrier molecule.'9 20 Regardless of the mechanism, interference with active transport reduces or abolishes the ea-pa,city of the cell to take up K and
extrude Na in an "uphill" direction at a rate
sufficient to compensate for the "downhill"
diffus;ion of the-se ions. The consequent, net
cellular K loss and Na uptake result in a decreased intracellular K concentration and an
increased intracellular Na concentration.
The Action Potential
The discussion to this point has. dealt with
the electrical potential difference during the
steady state prevailing in quiescent heart
muscle. It is expedient to consider next the
disturbances, of the steady state called action
potentials, the clinical counterparts of which
are the QRST complexes of the electrocardiogramn. The experimental observations, obtained with the intracellular microelectrode
technic, are comparatively simple (fig. 7).
The electrical potential difference across the
cell membrane of the resting mammalian ventricular muscle cell bathed in solutions having
the same K concentration as that of plasma
is between 80 and 90 millivolts, the interior
of the resting cell being negative with respect
to the extracellular solution. The action potential is propagated along the length of the
heart muscle-cell membrane. The electrical
potential difference across. the membrane is
observed to revers,e its electrical sign, changing from its resting value of -80 to -90 mV
to a value of +20 to +40 mV, the cell interior
becoming positive with respect to the extracellular solution. After the initial reversal,
the potential difference falls to its, resting
value with a delayed time course that results
in the characteristic plateau configuration of
the repolarization phase. It is instructive to
PAGE
9O7(
+20
0
POTENTIAL -20
DIFFERENCE
(millivolts) -40
O
3
-
-60
-80
-100
4
-
200 MILLISECONDS
-1
Figure 7
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Action potential of ventricular muscle cell. Phases
of action potential are numbered as follows:
(0) initial rapid upstroke or "spike"; (1) early
rapid repolarization; (2) slow repolarization or
"{plateau"; (3) terminal rapid repolarization; (4)
electrical potential difference across the cell membrane of quiescent cells or "resting potential."
Modified after Hoffman and Cranefield.29
eorrelate these observations with changes in
the permeability of the cell membrane to Na
and K. The significant experiments on which
this interpretation rests are the work of a
pioneer Swiss physiologist, Sylvio Weidmann.21-27 Weidmann 's contribution consisted
of the application of the theory of Hodgkini
and Huxley to Purkinje fibers from hearts of
large imanmmals. This theory deals with the
generation and conduction of the electrical
impulse and was developed by Hodgkin and
Huxley on the basis of extensive studies on
giant nerve fibers of marine invertebrates.28
For a detailed account of the electrophysiological research on heart muscle growing out
of Weidmaun 's observations, the reader is
referred to the appropriate reviews.29 30
The discussion that follows describes in
simplified formn, the changes, in electrical potential difference during the action potential
in terms of the ass,ociated permeability
changes. While changes in membrane pernmeability to ions can bring a-bout alterations in
the electrical potential difference, it is to be
emphasized that changes. in the electrical potential difference can themselves affect membrane permeability to ions.
In the steady state characteristic of resting
heart muscle cells the predominant " downhill" cation flux through the membrane is an
outwardly directed K diffusion, since the
resting nmembrane is permeable to K and relatively impermeable to Na. Moreover, in this
resting steady state there is no net ion current: the "downhill" outflux of K is returned
by an equal and opposite K influx and the
"downhill" influx of Na by an equal and
opposite Na outflux. By contrast, the course
of the action potential is characterized by
temporary imbalances between influx and outflux for Na and probably for K. These imbalances are reflected by a transient cellular
accumulation of Na early in the action potential and a probable transient cellular loss of K
during the repolarization phase.
The beginning of the action potential is
accompanied by a rapid increase of the pernieability of the cell membrane to Na, ions,
so that it beconmes much miore permeable to
Na thain to K. This permeability change is
observed whether the potential difference
across the membrane is allowed to fall spontaneously to the threshold for all-or-none
depolarizat,ion (" autorhythmicity ") or is
artificially lowered by passing an electric current across the membrane ("excitation "
(See Appendix 5). Whatever the mechanism
by which the increase in Na permeability is
brought about, its result is a greatly augmented Na,Cl influx as the Na ion moves
"downhill ' along its, electrochemical gradient. The permeability of heart muscle-cell
memtbrane to Cl ions relative to that for Na
can be shown to be rather small.'3 3, 32 Accordingly, the net inward diffusion of NaCl
resulting from the sudden increase of Na permeability sets up a diffusion potential tending
to make the intracellular face of the cell membrane positive with respect to its extracellular
face. This reversal of sign of the electrical
potential difference across the membrane
mneans that for a given thin section of the
membrane the advancing front of the net inward diffusion of Na.Cl is made up of positively charged Na ions, dragging behind them,
by the force of electrostatic at-traction, the
relatively impermeant Cl ions.. NaCl now
diffuses inward through the cell membrane
as, a dipole, the positive pole (the Na ion)
leading and the negative pole (the Cl iona)
Circulation. Volume XXVI, 0O-ober 1962
591
ELECTRICAL POTENTIAL DIFFERENCE
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f'ollowing. Since the membrane at the beginning of the action potential has been altered
to be many times more permeable to Na than
to K, the outward diffusion of KCl at this time
contributes eomparatively little to the observed potential difference. Figure 8 is a comparison of the res.ting steady state and the
first portion of the acetion potential with respect. to the dependence of the electrical potential difference on the external Na concent.ration. The figure shows that in the resting
state, when the membrane is relatively impermeable to Na, the potential difference remains unaffected by large changes in the external Na concentration. By contrast, during
the early part of the action potential there is
a marked dependence on the Na concentration, as indicated by the closeness with which
the slope of the observed potential difference
approaches the slope of the theoretical line
Vm = -61.5 log( [Na] i/[Na] o) for a. menbrane uniquely permeable to, Na. The import.ant differences in the permeability of the cell
membrane in the resting state, during the
early part of the action potential and during
repolarization are summarized in table 1.
The spike of the action potential (fig. 7),
corresponding to the increase in permeability
to Na just described, is of short duration. The
repolarization pha,se that ensues may again
be analyzed in terms of "downhill" and "uphill" transport. Considering first the "downhill" processes., we s.ee that the electrical
potential difference can be caused to shift
toward its resting value (intracellular solution negative) in either of two ways. A reversion of the increased Na pernmeability to
t,he relatively low value preva,iling in the resting state would reduce the net inward NaCl
diffusion and therefore also the associated
diffusion. potential that, makes the intracellular solution positive. Alternatively, even if
the Na permeability remains high, a transient
inerea-se in the K permeability above that obtaining at the beginning of the action potential would give rise to a net outward diffusion
of KCl. As, described earlier, such a net outward KCl movement would generate a diffuCirculation, Volume XXVI, October 1962
40co+
H
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uj
-
~~~~ACTIVE
~MEMBRANE
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20_
, ,
_
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o
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-
-
-
6 -80
RESTING
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C -100
100 150
50
8 10 15 20
% OF NORMAL EXTERNAL Na CONC.
Figure 8
Dependence of electrical potential difference across
active membrane (above) and resting membrane
(below) on external Na concentration. The broken
line is the value the potential difference would
have for a membrane exclusively permeable to
Na according to the relation Vm, = -61.5 log
The figure is taken from TVeidmann27 and describes experiments on Purkinje
fibers of dogs and goats.
([Na]j/[Na] j.
sion potentia,l tending to make the intracellula,r solution negative with respect t,o the cell
exterior. The studies of Weidmann suggest
that the repolarization phase includes both a
decreas.e in Na, permeability and a, transient
net. outward movement of K. A partial decrease in Na permeability appears, to occur
before the end of the spike, but the evidence
as, to whether the observed net outward KCl
movement is due to an increased K permeability is inconclusive. Weidmann suggested in
addition an explanation for the prolonged
plateau phase of slow repolarization. During
this phase the electrical potential difference
is temporarily maintained at a value intermediate between its steady state value and
the value at the time of the maximal depolarization (maximal intracellular positivity) at
the end of the spike. The plateau is interpreted as resulting from an adjustment of the
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Na and K permneabilities such that the diffusion- potential set up by the iniward net NaCl
diffusion is temporarily approximnately equal
to the diffusion potential of opposite electrical
sign generated by the niet outward diffusion
of KCI. Experimental evidence to support
this hypothesis has so far proved difficult to
obtain. The definitive determnination of the
magnitude and time sequence of the changes
in cation permeability durinig repolarization,
anid their exact correlation with particul-ar
segments of the action potential remain as
challenging unsolved problems.
"Uphill" transport during the repolarization phase includes the extrusion from the cell
of Na that has elntered during the period of
increased Na permeability, and the uptake by
the cell of K lost in any net outward K moveinents that may have occurred. The comparatively short duration of these transient permileability changes, as well as the relativelv
low inembrane permeability to Cl, probably
keeps cellular Na accumulationi small and limits cellular K loss. Nonietheless, the Na gain
anid K loss must be reversed by transport
against the electrocheinical gradient. For this
reasomi the portions of the action potential
associated with restoration of the steady state
should be sensitive to interference with the
active transport mechanisul, whether by oxygen lack, metabolic inhibitors, or digitalis
glycosides. It is not known at what point in
the repolarization sequence "uphill" transport processes become active, or whether restoration of the steady state is complete at the
time the electrical potential difference has
returned to its resting value.
The transient net ion movements associated
with the action potential should be accompamnied by net water movements, and therefore
by changes in cell volume. Moreover, complexities in the structure of the cell membrane33 and in the biophysical properties of
the extracellular regions of heart muscle7
raise the possibility of non-uniform ion distributions localized near the cell surface.
When methods for the experimental measurement of such distributions are developed, it is
Circulation, Volume XXVI, October 1.962
ELECTRICAL POTENTIAL DIFFERENCE
to be expected that the elemenitary scheme presented here may require modification.
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Summary
The electrica.l potential difference across
the cell membrane of heart muscle cells is a
diffusion potential aris,ing from the interaction
of fixed charges. within the membrane pores
with NaCl and KCI diffusing into and out of
the cell. The magnitude and sign of this potential difference depend on the relative permeabilities, of the membrane to K, Na, and Cl.
The resting membrane is predominantly permea.ble to K, while the action potential is
characterized by a transient increase in Na
permeability. An intracellular solution of
high K concentration and low Na concentration is separated by the cell membrane from
an extracellular solution having a low K concentration and a high Na concentration. These
concentration differences are maintained by
active transport processes. that utilize the
energy derived from cellular metabolic reactions to transport Na and K "uphill" against
electrical and concentration gradients.
References
1. TEORELL, T.: Transport processes and electrical
phenomena in ionic membranes. Progress in
Biophysics 3: 305, 1953.
2. KEDEM, O., AND KATCHALSKY, A.: A physical
interpretation of the phenomenologic coefficients of membrane permeability. J. Gen.
Physiol. 45: 143, 1961.
3. SOLLNER, K.: The electrochemistry of porous
membranes. In Electrochemistry in Biology
and Medicine, (T. Shedlovsky, editor), Newv
York, John Wiley and Sons, 1955, p. 33.
4. HELFFERICH, F.: Tonenaustauseher, Volume I,
chapter 8: Ionenaustauschermembranen. Weinheim/Bergstr. (Germany), 1959, p. 305.
5. MEARES, P., AND USSING, H. H.: The fluxes of
sodium and chloride ions across a cation
exchange resin membrane. Part 1-Effect of
a concentration gradient. Transactions of the
Faraday Society 55: 142, 1959.
6. MEARES, P., AND USSING, H. H.: The fluxes of
sodium and chloride ions across a cation
exchange resin membrane. Part 2-Diffusion
with electric current. Transactions of the
Faraday Society 55: 244, 1959.
7. PAGE, E.: Cat heart muscle in vitro. III. The
extracellular space. J. Gen Physiol. 1962. In
press.
Circulation, Volume XXVI, October 1962
593
8. FOLCH, J., LEES, M., AND SLOANE-STANLEY,
G. H.: The role of acidic lipids in the electrolyte balance of the nervous system of mammals. In Metabolism of the Nervous System
(D. Richter, editor). New York, Pergamon
Press, 1957, p. 174.
9. USSING, H. H.: The Alkali Metal Ions in
Biology. I. The Alkali Metal Ions in Isolated
Systems and Tissues. Handbuch der Experimentellen Pharmakologie, Ergainzungswerk,
Berlin, Springer Verlag, 1960.
10. DUNHAM, E. T., AND GLYNN, I. M.: Adenosinetriphosphatase activity and the active movements of alkali metal ions. J. Physiol. 156:
274, 1961.
11. SKOU, J. C.: The relationship of a (Mg2+ and
Na+) -activated, KR-stimulated enzyme or enzyme system to the active, linked transport
of Na4 and K4 across the cell membrane.
In Membrane Transport and Metabolism (A.
Kleinzeller and A. Kotyk, editors). New York,
Academic Press, 1961, p. 228.
12. PAGE, E., AND SOLOMION, A. K.: Cat heart muscle
in vitro. I. Cell volumes and intracellular
concentrations in papillary muscle. J. Gen.
Physiol. 44: 327, 1960.
13. PAGE, E.: Cat heart muscle in vitro. II. The
steady state resting potential difference in
quiescent papillary muscle. J. Gen. Physiol.
1962. In press.
14. SOLOMON, A. K.: Compartmenital methods of
kinetic analysis. In Mineral Metabolism, Volume I, Part A. New York, Academic Press,
1960, p. 119.
15. USSING, H. H.: The distinction by means of
tracers between active travsport and diffusion.
Acta physiol. Scandinav. 19: 43, 1949.
16. HARRIS, E. J.: Transport and Accumulation in
Biological Systems. Ed. 2. New York, Academic
Press, 1960.
17. KEDEM, O.: Criteria of active transport. In
Membrane Transport and Metabolism (A.
Kleinzeller and A. Kotyk, Editors). New
York, Academic Press, 1961, p. 87.
18. GLYNN, I. M.: The ionic permeability of th)e
red cell membrane. Progress in Biophysics
8: 241, 1957.
19. SOLOMnON, A. K., GILL, T. J., AND GOLD, G. L.:
The kinetics of cardiac glycoside inhibition
of potassium transport in human erythrocytes.
J. Gen. Physiol. 40: 327, 1957.
20. GLYNN, I. M.: The action of cardiac glycosides on sodium and potassium movements in
human red cells. J. Physiol. 136: 148, 1957.
21. DRAPER, M. H., AND WEIDMANN, S.: Cardiac
resting and action potentials recorded with
an intracellular electrode. J. Physiol. 115:
74, 1951.
594
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22. WEIDMANN, S.: Effect of current flow on the
membrane potential of cardiac muscle. J.
Physiol. 115: 227, 1951.
23. WEIDMANN, S.: The electrical constants of
Purkinje fibers. J. Physiol. 118: 348, 1952.
24. COREABOEUF, E., AND WEIDMANN, S.: Tenmper ature effects on the electrical activity of
Purkinje fibers. Helvet. physiol. acta 12: 32,
1954.
25. WEIDMANN, S.: The effect of the cardiac membrane potential on the rapid availability of
the sodium-carrying system. J. Physiol. 127:
213, 1955.
26. WEIDMANN, S.: Effects of calcium ions and
local anesthetics on electrical properties of
Purkinje fibers. J. Physiol. 129: 568, 1955.
27.
1NEIDMNN, S.: Elektrophysiologie der Herznmuskelfaser. Berin, Mediziniseher Verlag Hans
Huber, 1956.
28. HODGKIN, A. L.: The Croonian Lecture: Ionic
atovements anid electrical activity in giant
erive fibers. Proc. Roy. Soc., Ser. B. 148:
1, 1958.
29. HOFFMAN, B. F., AND CRXNEFIELD, P. F.: Electrophysiology of the Heart. New York, McGraw
Hill Book Co., 1960.
30. CORABOET Fi, E.: Aspects cellulaires de 1'6lectrogenese cardiaque clez les vrte6br6s. J. Physiol.,
Paris 52: 323, 1960.
31. HUTTER, 0. F., AND NOBLE, D.: Anion conductance of cardiac nmusele. J. Physiol. 157:
335, 1961.
32. CARMEI.ET, E. E.: Chloride ions arid the membrane potential of Purkinje fibers. J. Physiol.
156: 375, 1961.
33. SiMpsoN, F. 0., AND OERTELIS, S. J.: The fine
structure of sheep inyocardial cells; sarcolemmal invaginiations and the transverse tubular
system . J. Cell. Biol. 12: 91, 1962.
34. STERN, K. H., XND Amis, E. S.: Iontic size.
ChemB. Reviews 59: 1, 1959.
35. ROBINSON, R. A., A-ND STOKES, R. H.: Electrolyte
Solutions. Ed. 2. New York, Academic Press,
Inc., 1959, p. 11.
36. EISENATAN, G., RUDIN, D. O., AND CASBY, J. U.:
Glass electrode for measuring sodium ion.
Science 126: 831, 1957.
37. IHINKE, J. A. M.: The measurement of sodium
anld potassium activities in squid axon by
meanls of cation-selective glass micro-electrodes.
J. Physiol. 156: 314, 1961.
38. GOLDMAN, D. E.: Potential, impedance and
rectification in membranes. J. Gen. Physiol.
27: 37, 1943.
39. HODGKIN, A. L., AND KATZ, B.: The effect of
sodium on the electrical activity of the giant
axon of the squid. J. Physiol. 108: 37, 1949.
PAGE
Appendices
1. The electrical potential difference
across a
membrane may include, in addition to the diffusion potential described above, a contribution from
so-called Donnan potentials due to fixed eharges
at the boundary of the nmnembrane with the solutions on either side.1 In order to simplify the
present discussion, such Donnan potentials are
considered negligible.
2. The use of the K concentrations in this
equation is an approximation. To be exact, the
concentration terms [K] should be multiplied
by a factor, y, called an activity coefficient, the
product y [K] being defined as the activity of
K in the solution. The activity may be thought
of as an effective conicentration, i.e., as that fraction of the total K concentration which is effective in producing an electrical potential difference.
At the concentrations encountered in tissue fluids,
the activity of ions is always less than their
concentration. The usual flamle photometric determiination of K and Na nmeasures concentrations.
The K and Na activities of solutions may, however, be measured directly with special K and Na
glass electrodes,36' 3 just as the activity of hydrogen ion is conventionally measured with a pH
glass electrode.
3. In deciding for a given biological membrane
whether the transport of a charged particle like
the K ion is an "aetive," "uphill" or energyconsuming process rather than a "passive," "downhill" or spontaneous process it is necessary to
take into consideration not only the gradient of
concentration but also the gradient of electrical
potential. Thus, movement of K from an extraeellular coneentration of 5 mM into a cellular
solution at a concentration of 200 mM is "uphill"
with respect to the concentration gradient; since
the cellular solution is at a negative electrical
potential coiipared with the extracellular solution,
the transport into the cell of positively charged
particles like the K ion is, however, "downhill"
with respect to the gradient of potential. When
both concentration and potential gradients are
considered together for the siniultaneous movernents of K and Na, it appears likely that both
these ions are actively transported in mammialian
heart muscle. Throughout this paper the conventional assunmption that the Cl ion is passively
transported is followed. A consequence of this
assumption is that in the steady state at 370
C the distribution of Cl ions between the intracellular and extracellular solutions can be predicted
from the electrical potential difference across the
cell membrane by the relation, Vm = -61.5 log
([Cl] 0/[Cl] i). For a discussion of the validity
of this assunmiption, see Page.7
Circulation, Volume XXVI, October 1962
ELECTRICAL POTENTIAL DIFFERENCE
4. An approximationi com-monly used to express
these relative contributions is the equation developed by Goldman38 and by Hodgkin and Katz.39
If movements of Cl may be assumed to be passive, this equation takes the form,
Vm = -61.5 log pK [K]i +
PNa [Na]
Downloaded from http://circ.ahajournals.org/ by guest on September 30, 2016
in which Vm is the electrical potential difference
across the cell membrane at 370 C, [K] i and
[Na]i are the intracellular K and Na concentrations, [K] 0 and [Na] 0 the corresponding extracellular concentrations, and PK and PNa the permeabilities of the membrane to K and Na, respecttively.
5. Changes in the a.pparently small electrical
potential differences across cell mnembranes of
excitable tissues may alter the permeability of the
membrane to ions because the short distances
across which such potential differences exist set
up relatively large forces. The force aeting on a
charged particle in the membrane is called an
595
electric field and may be approximated by the
electrical potential difference divided by the thickness of the membrane. For an electrical potential
difference of 100 mV across a cell membrane
100 A in thickness this calculation gives a force
of 100,000 volts per centimeter. In an electric field
of this magnitude positively charged molecules
within the substance of the membrane will tend
to move toward the negatively charged face of
the membrane and negatively charged molecules
will attempt to migrate to the positively charged
face. Since the charged molecules making up the
substance of the memnbrane are fixed, they are
prevented from moving in these directions. Such
molecules, however, may have a certain amount
of freedom to rotate about an axis. This freedom
permits them to orient themselves so that their
fixed charge groups tend to point toward the
face of the memubrane toward which they would
migrate if they were free to move. Variations in
the electrical potential difference may alter this
orientation of fixed charges, suggesting a possible mechanism for permeability clhanges.
If our feeling constantly puts the question why, our reason shows us that only the
question how is within our range; for the moment, then, only the question how concerns
men of science and experimenters. If we cannot know why opium and its alkaloids put
us to sleep, we can learn the mechanism of sleep and know how opium or its ingredients
puts us to sleep; for sleep takes place only because an active substance enters into
contact with certain organic substances which it changes. Learning these changes will
give us the means of producing or preventing sleep, and we shall be able to act on the
phenomenon and regulate it at pleasure.-CLAUDE BERNARD. An Introduction to the Study
of Experimental Medicine. New York, The Macmillan Company, 1927, p. 82.
Circulation, Volume XXVI. October
1962
The Electrical Potential Difference Across the Cell Membrane of Heart Muscle:
Biophysical Considerations
ERNEST PAGE
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Circulation. 1962;26:582-595
doi: 10.1161/01.CIR.26.4.582
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