Published May 1, 1960
The Interpretation of Selective Ionic Permeability
and Cellular Potentials in Terms of
the Fixed Charge-Induction Hypothesis
GILBERT NING LING
From the Department of Basic Research, Eastern Pennsylvania Psychiatric Institute,
Philadelphia
x For a comprehensive review of the older literature as well as an impressive amount of more recent
Russian work the reader is referred to Troschin's book, Das Problem der ZellperrneabilitNt (1958).
I49
The Journal of General Physiology
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Muscle and nerve possess two closely related properties that are of interest
to the physiologist: a labile electric potential difference across the cell surface
and the ability to accumulate selectively potassium from an environment poor
in that cation but rich in sodium. It appears that most investigators primarily
interested in the electric potential have adhered to the original concept laid
down by Ostwald (1890), McDonald (1900), and Bernstein (1902) that the
electric potential arises basically from a difference in permeabilities toward
different ions. Such a differential ionic permeability, in turn, arises from the
semipermeability of a unique cell membrane separating an intraeellular
dilute solution of proteins and salts and the extracellular fluid, another dilute
solution of similar composition. O n the other hand, investigators in the field
of ionic accumulation have been far from unanimous in accepting this membrane theory as an explanation of asymmetric ionic distribution. A large
school of them have come to believe that the K + ion selectively accumulated
in muscle and nerve cells for instance, is due to potassium ion binding within
the cell (Neuschloss, 1926; Troschin, 1958~; Shaw and Simon, 1955; Menozzi
et al., 1959). All in all, one can probably say that the proponents of the membrane theory have thus far presented a more persuasive set of arguments.
For it has undoubtedly dominated the thinking in this field. A major weakness
in the bound potassium concept lies in the general implication that "binding"
is an irreversible process. Thus bound potassium was expected never to diffuse
out of the cells even after the ceils are ground to a pulp. This expectation is
simply not experimentally supported (see following discussion on K + ion
binding of actomyosin). But even if one proposes a hypothesis including a
labile reversible process there are other obstacles to overcome.
Physiologists in their attempt to understand living phenomena must draw
upon well established physicochemical laws and models to explain the
behavior of their less understood material. For the mechanism of electric po-
Published May 1, 1960
15o
PHYSIOLOGY
OF CELL MEMBRANE
tential differences occurring between two ionic phases physiologists have
generally based their thinking on the theory established by Nernst (1889),
Ostwald (1890), Donnan (1911), and Donnan and Guggenheim (1932). The
prototype is that of Ostwald's copper ferrocyanide precipitation membrane
which gives rise to a potential difference between the two solution phases the
membrane separates. T h e theory is, as is well known, an established part of
the material taught in a thermodynamics course. Perhaps for this reason alone,
the very existence of a cellular potential tends to discourage any bound K +
ion concept as a mechanism for selective accumulation. For the Nernst equation states that this membrane potential,
Rr
'
Rr,
~, = - ~ - In a x = -P-
A[K],
(1)
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in which a~, f~:, [K]~ are the activity, activity coefficient, and the concentration of K ion in the intracellular phase, a~, f~, [K]o are those in the extracellular phase. Now the activity coefficient, an index of the non-ideality of
K + ion, is a measure of K + ion binding. Since [K]~, fix, [K]o are determined or
known, f~ can be computed from the measured value of ~k at absolute temperature T. Such a simple calculation shows that fl~ must be almost the same
as f~:. Some sort of disproof of the bound potassium concept is thus obtained
on the basis of the Nernst equation and the size of the measured potential.
A second apparently convincing evidence against the bound K + ion concept
appears even more direct. In cells the only components that are concentrated
and ubiquitous enough to bind the K + ions are proteins. Yet all attempts to
show a high degree of selective K + ion accumulation by such isolated cellular
proteins as actomyosin have failed although K + and Na + ion binding on some
proteins is well established (Szent-Gy6rgyi, 1947; Lewis and Saroff, 1957).
This failure to find a selective ionic binding is also expected on the ground of
the major hypothesis of ionic interaction of proteins--the LinderstrCm-Lang
theory which is a direct application of the Debye-Hfickel limiting law of ionic
solutions (1923). The major assumption in this theory is such that no specific
ionic association is expected between such ions as K + and Na + and the proteins.
In 1951 and 1952 the author published the original version of his fixed
charge hypothesis in which it was suggested that the living cell may not be a
sac containing an aqueous solution of salts and proteins. But that the densely
packed cellular proteins are highly organized as shown by the x-ray diffraction pattern of muscle cells (Astbury, 1939). The high density of charges
carried by the trlfunctional amino acids are thus fixed in space. The hypothesis assumed that association between oppositely charged ions becomes
tremendously increased if one species of the ion is fixed in a macroscopic
Published May 1, 1960
LInG Selective 1ohio Permeability and Cellular Potentials
x5I
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three-dimensional latticework. Selective ionic accumulation follows from a
difference in the electrostatic energy between the fixed charges and the interacting ions. In this early treatment the simple assumption was made that the
fixed anionic charges in living cells are predominantly carboxyl groups carried
by aspartic and glutamic residues of the proteins and that they are unvarying.
The electrostatic interaction energy then would be determined by the average
dielectric constant and by the "distance of closest approach" between the
fixed anion and the cation. Assuming then that the "distance of closest approach" was determined by the hydrated radii of the competing cations, a
demonstration of selectivity in K + ion accumulation over Na + ion was possible
(Ling, 1952).
Though following events seemed to support the view that the cell was a
fixed charge system, any illusions on the part of the author that this model for
selectivity was generally applicable to all living and non-living fixed charge
systems were short-lived. For it soon became clear that the model was incapable of explaining an increasing amount of evidence for the existence of
alkali metal ion adsorption in sequences other than that of the hydrated
diameters. In retrospect we know that the key to the successful resolution of
the problem of cation specificity already existed. Implicit in Wiegner and
Jenny's (1927) and in Jenny's (1932) suggestion that in clays and permutits
dehydration of the cation produces various "irregular" orders, and more
explicitly in Bungenberg de Jong's, (1949) consideration that a variation of
the polarizability of the anion, creating what he called "transition sequences"
(1949, p. 289). However, it is towards his present colleagues, Eisenman,
Rudin, and Casby that the author owes a special debt of gratitude for these
investigators predicted (Eisenman, Rudin, and Casby, 1957; Rudin and
Eisenman, 1959) and brought to his attention the fact that variation of the
"anionic field strength" leads to particular order of ionic selectivity, and that
this pattern has wide distribution in nature. It was this revelation that led
the author to construct a new microscopic model (1957). In this model all
known physical forces, including Coulomb's and van der WaN's, and other
energies were taken into account in a calculation of the adsorption energies
of the various cations (see change b below).
There are three major changes made in this revision:
(a) Instead of presenting as an assumption the assertion that fixation increases the association of a charge's counterion, an explicit mechanism is now
given in terms of statistical mechanics. The predicted increase of ionic association with fixation of one species of ion provides some possible answers
to both of the fundamental difficulties confronting the adsorption concept
discussed above; i.e., the lack of a theory for potential differences between
two ionic phases and the failure to demonstrate selective ionic adsorption in
isolated protein solutions.
Published May 1, 1960
152
PHYSIOLOGY
OF CELL MEMBRANE
T h e Significance o[ Charge Fixation u p o n Counterion Distribution
The association between A and B, like all reactions, is determined by the free
energy change involved in this process
A -b B ~ A . B Jr AG°
=
[A],.,.°
[A]d,... [B]d,,,o. = exp
(--aC°/Rr)
(2)
(a)
However, the standard free energy change AGo involves both a standard heat
eontent change A H ° and a standard entropy change T A S ° and the latter can
be as important as the former in determining the equilibrium constant, K.
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(b) Neither the fixed ions nor their countereations are regarded as unvarying.
Instead, the fixed protein carboxyl groups are allowed to vary what may be
loosely called their effective charge but is more rigorously defined as their
c value (see below). The cations are not assumed to have any definite hydrated
diameter, rather a statistieally varying n u m b e r of water molecules are interspersed between the fixed anions and the free cation and these are permitted
to vary with both the c value of the anion and the nature of the eation investigated.
(c) The c value of the anion will vary in response to changes on the protein
molecule at some distance. It was proposed (for abstract, see Ling, 1957; 1958)
that such a long range interaction is made possible by the high polarizability of the
resonating polypeptide chain "backbone" and through the combined action of the induction and the direct electrostatic effects of the adsorbed counterions. The induction and
direct electrostatic effects are collectively termed the direct F effect. An important variation of this direct F effect, called an indirect F effect, is
visualized to enable protein molecules to propagate an electronic change to
points beyond those reached by the direct induction and direct electrostatic
effects. The revised fixed charge hypothesis is no longer limited to dealing
with static problems but, by the induction effect, describes also changes in
the fixed charge system (for abstract, see Ling, 1958). For this reason the
revised theory now bears the name, the fixed charge-induction hypothesis.
The thesis, no longer confined to selective ionic accumulation, permeability,
and the electric potential, has been extended to cover many aspects of physiological events at the molecular level. It will be published shortly as a monograph entitled "A Theory of Physiological Activity at the Molecular Level-the Fixed Charge-lnduction Hypothesis." While the author must refer to this
monograph for details of the complete hypothesis, to make our later discussion
intelligible we shall proceed as succinctly as possible to discuss some salient
features of the revision just mentioned.
Published May 1, 1960
LInG
Selective Ionic Permeability and Cellular Potentials
I53
AG ° = A H o -- T A S o
(4)
T h e fact t h a t ice c a n s u b l i m a t e into v a p o r w i t h o u t m e l t i n g first a t a subzero
t e m p e r a t u r e is chiefly d u e to the larger e n t r o p y gain o n e v a p o r a t i o n t h a n
o n liquification. Statistical m e c h a n i c s w h i c h provides a n explicit i n t e r p r e t a tion of e n t r o p y , relates it to the p a r t i t i o n functions z of e a c h of the i n t e r a c t i n g
species in e a c h o f the possible states so t h a t E q u a t i o n (3) c a n be w r i t t e n as
X-
.,oo
P~ai.o. P~ai.oo exp ( - - , t d - I ° / R T )
(5)
K -
V~,,~ V.~,,~ exp ( - ~r-I°/R T )
V2i.o. v i...o
(6)
T h u s a n undissociated w a t e r m o l e c u l e in ice has little free volume. I n liquid
w a t e r it has a larger free v o l u m e so ice m e l t s at a b o v e zero t e m p e r a t u r e s .
T h e e v e n larger free v o l u m e , e q u a l to the v o l u m e of the total u n o c c u p i e d
e m p t y space a r o u n d it, allows ice to s u b l i m a t e at below m e l t i n g t e m p e r a t u r e .
I n a n ionic association process o c c u r r i n g in a solution at c o n s t a n t v o l u m e
the H e l m h o l t z free e n e r g y AF° a n d the i n t e r n a l e n e r g y A E o m o r e a d e q u a t e l y
describe the e q u i l i b r i u m a n d we have, instead of E q u a t i o n s (4) a n d ( 6 )
(7)
AF ° = AE°--TAS °
K~-
a
Vg.°o
V8
u.o. e x p ( - -
v2,..o° v2,..oo
AEO/RT)
(8)
2 If one tosses a coin, the statistical probability of getting a " h e a d " as getting a "tail" is equal. H o w ever, ff one manufactures a coin that has one " h e a d " but, let us say five "tails" (like a dice), t h e
probability of getting a "tail" would be five times as high ~ getting a " h e a d . " I n ionic association
we again encounter a statistical p h e n o m e n o n . I t is only at absolute zero temperature t h a t t h e r e is
only one energy level corresponding to the associated and another to the dissociated state; their
energy difference is then equal to A E °. As temperature rises, the q u a n t u m - m e c h a n i c a l l y allowed
energy levels, that the ions can occupy, increase but usually at different rates for the associated state
and for the dissociated state. The total number of these levels corresponding to each state is called
the partition function of that state, e.g., P,,,oo or Pdt,o0. Their importance in determining the statistical distribution of ions in the associated or dissociated state is entirdy similar to the number of
"heads" and "tails" in determining the probability of getting a "tail" or a "head" in tossing a coin
(Gurney, 1949; Fowler and Guggenheim, 1939).
s This frec volume refers to that volume in the aqueous solution that is occupiable by an ion where
the water is considered as a continuous dielectric. In this sense it differs from the conventional
"free volume" of liquid state, denoting the volume not actually occupied by the molecules.
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T h e p a r t i t i o n f u n c t i o n for e a c h state is a p r o d u c t o f several p a r t i t i o n functions
r e p r e s e n t i n g the different d e g r e e s of f r e e d o m : translational, rotational, vib r a t i o n a l , a n d electronic. F o r simplicity, we shall focus o u r a t t e n t i o n o n o n l y
the p a r t i t i o n f u n c t i o n w h i c h is most i m p o r t a n t for the present case. T h i s is
the translational p a r t i t i o n f u n c t i o n w h i c h is directly r e l a t e d to the " f r e e
v o l u m e ''3 of t h a t species in t h a t state. W e can t h e n simplify E q u a t i o n (5) to
read
Published May 1, 1960
P H Y S I O L O G Y OF C E L L M E M B R A N E
I54
This tells us that if A E °, Va~noo, Vn,0,ooare all constant, the degree of dissociation
is determined by the free volumes of the dissociated species.
F r o m the electrolyte theory of Bjerrum (1926) it can be derived that the
free volume for the dissociated state is equal to the reciprocal of ionic concentration C in an electrolyte solute in which
i_
C
V
N~
(9)
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in which V is the total volume of the solution and N ± refers to the total n u m ber of cations as well as anions. T h e free volume is thus equal to the average
volume that a positive or negative ion occupies (see monograph to be published). In agreement we know that in an infinitely dilute solution the degree
of association is nil as Vdi,,o~ --> 0o. As concentration increases the free volume
falls. The decrease of free volume then leads to an increase of ionic association
as is well testified by the fall of activity coefficients. T h u s whether ions such
as K + or Na + remain dissociated as in infinitely dilute aqueous solutions or
associate under different conditions depends on the free volume of the dissociated state of the counterion. By fixing the ionic groups onto a threedimensional lattice, it becomes possible for a constant high density of charges
to be maintained, while in equilibrium with external solutions, the ionic
concentrations of which m a y be a great deal lower. By Equation (8) such a
high fixed charge density will favor a constant high degree of ionic association. This is, however, not the only mechanism by which charge fixation
could increase the counterion association. Thus Equation (9) applies only to
dilute solutions. As the total ionic concentration increases the simplification
Vdi,,oo = -V/Nq- becomes less and less accurate for two reasons: Firstly in
free solution all ions are constantly moving and there are no stable energy
barriers limiting the passage of ions from one such "private territory" to
another. I n consequence Vdi,,o, should include an additive value equivalent
to that shared by more than one ion. We shall refer to this as the "extramicrocell free volume" V,zt, m. Secondly as ionic concentration increases the
free volume for the associated state V,,,oo is no longer negligible. Thus we
arrive at the conclusion that Vdi,,oo = ( V / N ± -- V,,,oo) "b V,~t,m. T h e
term V / N ± will be referred to as the "microcell free volume."
A careful evaluation of the amino acid compositions of cell proteins has
led to the conclusion that all living ceils, irrespective of the type of tissue o r
the species of organism, possess fixed anionic and cationic charges at an average density of one site every 20/~ in a three-dimensional system (Fig. I, see
monograph). A cell endowed with such a large n u m b e r of charges is a macroscopic fixed charge system. As such it must maintain its macroscopic electroneutrality. I n other words, except for the relatively few counterions on the
cell surface most counterions must stay within the cell. T h e dissociation of
the majority of the counterions like K + in such a fixed charge system is not a
Published May 1, 1960
Lmo
Selective Ionic Permeability and Cellular Potentials
I55
question of dissociation into the outside solution but to other positions still
within the macroscopic fixed charge system which we shall refer to as interstitial positions.
X-ray diffraction of muscle cells have shown that the proteins in these cells
are not randomly distributed but occupy definite positions in space (Astbury,
1939). Thus the charges carried on the proteins in the ceUs are fixed in space
at a high density like charges carried by say, Na + and CI- ions in a salt crystal.
The quasipermanent energy barriers (see Fig. 6) thus greatly limit the excursions of a counterion from one microcell to another and thus reduce the extramicroceU free volume. I n this the free volume begins to approximate the microceU free volume minus the volume occupied by the associated ion pair. In
consequence, the free volume for a counterion in the dissociated state within
the fixed charge system is not m u c h greater than that in the associated state.
",_ ~
~
.
polyl~eptide'"
"bockbone"
fixedonion
'
~
l
.
..-"
/
fixed
ohon
", ~
"~ic rocells
F ] o u ~ I. A hypothetical scheme of the cell
surface and bulk phase consisting of microcells
which surround each fixed charge group. The
average distance is 20 ~k from the center of one
microcell to the center of the next,
It follows that at even a rclativclylow cncrgy of adsorption nearly complctc
association of countcrion and the fixed charges occurs.
Summarizing, wc conclude that the cffccts of chargc fixation upon ionic
associationarc twofold although thcsc arc not sharply scparablc: to prcscrvc a
low microccU-frcc volume by insuring a constant high ionic dcnsity; and to
rcducc extramicroccll-frccvolume.
The Definition oJ c Value and the Calculation of the Variation o[
Ionic Selectivity with c Value oI the Anionic Groups oJ the Fixed
Charge System
It is a well known fact that acetic acid is a weak acid and that trichloroacetic
acid, the familiar protein denaturant, is a strong acid. In other words,
while the carboxyl group of acetic acid has a strong affinity for its proton,
that of trichloroacetic acid is relatively weak. Yet these two molecules differ
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]
z
Published May 1, 1960
I56
PHYSIOLOGY
OF CELL
MEMBRANE
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only in the nature of the three substituent atoms located a distance away
from their respective functional carboxylic groups. This means that induction
and direct electrostatic effects of the more electronegative chlorine atoms
(i.e., in the molecule the chlorine atom has a greater power to attract electrons
to itself, Pauling, 1948, p. 58) d r a w electrons more effectively away from the
carboxyl oxygen than do the hydrogen atoms so that the electrostatic interaction between the negatively charged carboxyl groups and the positively
charged proton is diminished. A strong acid is thus m a d e from a weak one
b y a substitution occurring at some distance from the reactant group (see
Branch and Calvin, 1944).
T h e c value is a measure of the magnitude of this effect. While a complete
definition is reserved for the forthcoming book it is sufficient for present
purposes to state that the ¢ value is an arbitrary parameter given in ~mgstrom
units (see Fig. 1) and that a strong acid like trichloroacetic will have a lower
c value (e.g., - 3 . 0 / ~ ) than a weak one such as acetic acid (e.g., --1.0 ~).
I n the model used to calculate variation o f ionic selectivity w i t h C value
we carve out a cylindrical cavity around the end of a protein carboxyl g r o u p
and insert none, one, two, or three water molecules between the carboxyl
oxygen and a specific cation in a linear array. These are called configurations
0, I, II, and I I I respectively (Fig. 2).
T h e total energy of each of these configurations is then computed for the
ions, H +, NH~+, Cs +, R b +, K +, Na +, and IA+. I n this calculation all known
non-exchange energies are taken into account which include the Coulomb
energy, Debye energy, Keesom energy, London energy, Born repulsion energy,
etc.
T h e results give us the statistical distribution of these configurations as a
function of c value and the specific countercation. This permits the calculation
of the adsorption energy of each species of cation as a function of ¢ value by
the Born-charging method. The result is illustrated in Fig. 3 in which the
polarizability of the anion is taken as 0.876 X 10"-24cm. 3. T h e curves in Fig. 3
show that as the c value varies, the ionic preference varies with it. However,
the rank orders of preference shown in Fig. 3 are not unique; other orders
are created when the anionic polarizability changes. At all values of polarizabilities considered it is generally true that a fixed carboxyl group preferring
the K + ion m a y change its preference to that of selecting Na + ion in consequence of an interaction at a distant site through the operation of the direct
and indirect F effects.
A proper exposition of the F effect is too involved for inclusion in this
paper. For the present it will suffice to state that the c value change at site II
can be brought about by the F effect in consequence of an exchange of partners at a neighboring site I. The resultant shift in counterionic preference
leads to an exchange at site II. This exchange in turn, affects the c value of a
Published May 1, 1960
Lmo
Selective Ionic Permeability and Cellular Potentials
z57
third site I I I with a consequent exchange. Such a "falling domino" effect
may propagate a c value perturbation a considerable distance from its origin.
This long range effect on c value is called the indirect F effect, and the process,
the indirect F process (for abstract, see Ling, 1958). In the monograph forthcoming the thesis will be presented that while the direct F effect may explain
L
e
_1.
d
.I.
g
,I
Configuration
0
Configuration
I
"IT
Fzoum~ 2. The linear model. The shaded circle on the left in each configuration represents the negatively charged oxygen atom of an oxyacid (e.g., earboxyl) and the shaded
circle on the right represents its countercation. Empty circles represent water and the
various letters denote distances used in the computations.
such non-competitive type of protein interaction as observable in enzyme
kinetics the indirect F process underlies the all-or-none type of protein changes
seen in denaturation, in muscle contraction, etc.
Having given a bird's-eye view of the basic revision as well as new concepts
introduced into the original hypothesis, we shall devote the remainder of this
paper to a brief discussion of two specific subjects, cellular potentials and
selective ionic permeability. According to the membrane theory selective
ionic permeability is the cause of cellular electrical potentials while the fixed
charge induction hypothesis maintains that both phenomena arise as attributes of fixed charge systems. As such, selective permeability is related to
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Configurotion
Published May 1, 1960
158
PHYSIOLOGY
OF CELL MEMBRANE
the potential but is not its cause. By discussing these two topics it is hoped
that we can at once give an illustration of the general nature of the fixed
charge-induction hypothesis and relate the hypothesis to the topics of the
present symposium.
/
#
4
", = 0 . 8 7 6 x 10-=4 cm3
//
I
s
"
~20i
)
.
.
.
.
,,-
.÷
I
251
.
.
/
r
/
/
Iq~t
¢
r/
15
~7
.9
=
O
,m~
~
.,
I
.v...~ i
;~ I 0
• ..
.-"
5.0
4.0
/
//
x
'I
,~.=.,_ ........ ~ i .
t=
/
~/~'/" /i
IF.,,
i! ,
'i
I
I
d.
I
...t
3.0
2.0
L0
- c (J,)
FiotraE 3. The computed dissociation energies of various cations when the fixed
anionic groups has a polarizability a, of 0.876 X 10-~a cms. The meaning of c value is
given in the text.
C E L L U L A R RESTING AND ACTION P O T E N T I A L
T h e Nernst equation, applied to muscle and nerve cell potentials, bears the
simple form of Equation (1) (Bernstein, 1902; McDonald, 1900). In recent
years considerable evidence has accumulated to support the prediction that
the potential does vary with the absolute temperature (Ling and Woodbury,
1949; Hodgkin and Katz, 1949b) and logarithmically with the external K +
ion concentration, [K]o (McDonald, 1900; Cowan, 1934; Curtis and Cole,
1942; Ling and Gerard, 1950; Huxley and Stfimpfli, 1951). The validity of
the equation, however, depends on the assumption of an absolute Na + ion
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i
!
Published May 1, 1960
Ln~o
Selective Ionic Permeability and Cellular Potentials
I59
impermeability of the cell membrane, an assumption which has been proved
to be wrong (Heppel and Schmidt, 1938; Steinbach, 1951). Accordingly, the
Nernst equation, if it is to apply, should be more correctly written as:
~b = /~- f In
[Na], + [K],
[Na], + [K.lo
(m)
RT In Px[K]~ + PN,[Nal~ + PcI[CI]o
P~K]. + P~[Na]o + Po,[Cl]~
(11)
relating the potential to the relative permeability of Na +, K +, and CI- ions
respectively represented as P~,, Px, and Pcl. Variations of these permeability
constants in this equation are found to give values of the potential comparable
to those measured at rest (resting potential) and during activity (action
potential).
A difficulty of the membrane potential theory is the failure to demonstrate
a correlation between the macroscopicaUy measured intraceUular K + ion
concentration and the potential demanded by both the original Nernst
Equation (1) and the newer Equation (11).
(a) The expected rise of potential was not observed following the microinjection of concentrated solutions of K + salts into muscle and into nerve
fibers (Grundfest, Kao, and Altamirano, 1955; Falk and Gerard, 1954).
(b) No resting potential could be measured in Funduluseggs although high
concentration gradients of both potassium and sodium are found across their
cell surfaces (K~ = 105-I 17 m~/liter, Ko -- 10 re_M/liter; Na~ --- 50 raM/liter;
Nao = 452 mu/liter) (Kao, 1956).
(c) No correlation was found between the resting potential of frog muscle
and its K + content nor between the intracellular Na + ion content and the
size of the measured "overshoot" of the action potential (Shaw and Simon,
1955; Shaw, Simon, and Johnstone, 1956).
Collectively, the evidence shows that the measured potential does not
depend upon the gross internal K + ion concentration. While the membrane
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but since [Na]i + [K]~ is approximately equal to [Na], + [K], (for values,
see Hodgkin, 1951) there should be no potential whatever. A substantial
potential definitely exists. Discarding the older view of absolute impermeability to the Na + ion, the maintenance of a low intracellular Na+ ion concentration was delegated to the operation of a metabolic pump (Dean, 1941;
Krogh, 1946; Hodgkin, 1951; Hodgkin and Keynes, 1955). The shortcomings
of this hypothesis have been twice reviewed by the author and are not to be
further discussed here (Ling, 1952; 1955a). In line with the membrane-pump
theory, Hodgkin and Katz (1949a) applied Goldman's equation (1943)
and wrote
Published May 1, 1960
I60
PHYSIOLOGY
OF
CELL
MEMBRANE
[K]i.~, = [ K ] . . . ~
exp
(A~/2RT)
( 12 )
Similarly,
[Nal,nt, = [NaJ,,o0 ~
exp
(A~,/2RT)
( 13 )
These dissociations will contribute nothing to the macroscopicelectric potential
across the surface of the fixed charge system.
However, there exists another equilibrium: that between the interstitial
ions and those ions in the free external solution, This is described by
[K]o = [Kli.,, ~SSOO
~
exp
-
-
(--~b/RT)
(14)
exp ( - - # / R T )
( 15 )
,t intn
[Na]o = rivaling, ~
I ints
in which ~b is the surface potential (e.g., resting potential). Since in earlier
consideration we have shown that Pi,t./P,,oo is not very large, at the appropriate c value almost all ions are adsorbed. Consequently if we represent the
concentration of fixed anionic sites on the fixed charge surface as If-] then
[K]..oo + [Na],,oo = [f-].
Based on these relationships one can derive an equation for the potential
(z6)
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theory is thus directly contradicted, the fixed charge-induction hypothesis
permits a conciliation of these experimental findings with the evidence that
up to now has been considered more or less unique supports for the m e m b r a n e
potential theory, namely that the potential covaries with absolute temperature
and with the external K + ion concentration [K]o. To demonstrate this we
shall first derive an equation for the cellular potentials according to the present
hypothesis.
As pointed out previously, an ion within a fixed charge system can exist
either as an adsorbed ion occupying a site with its partition functions, P,,o~
or as a dissociation ion, still within the macroscopic fixed charge system, but
occupying an interstitial position with its partition functions, Pin,. F r o m the
definition of interstitial position it is obvious that an adsorbed ion can migrate
from one position to another only after having temporarily taken an
interstitial position. The relation between the concentration of adsorbed K +
ion [K].~,oo, and the concentration of interstitial K + ion, [K] ints, can be written
as (see Frenkel, 1926;Jost, 1933).
Published May 1, 1960
LINO SelectiveIonic Permeabilityand CellularPotentials
x6t
If we make the simplifying assumption
p .oo =
P ,8o0 =
(17)
:oo = P,**o
(18)
= Pd ..o0
Equation (16) may be written as
RT In f
EK]oexp \ 2--2~}
F
,k = _R_~ln[/_-] _ R~_ in P,,....
Paissoe
(19)
+ [Na~o exp \2-ffR-T--] 1
Recalling the linearity of c- AEo plot shown in Fig. 3, for a short range of
c value variation, the approximation may be made
(20)
~.
(21)
= As.c + B~.
which when substituted into Equation (19) renders
¢ ' = ~ - ~ ln[f-] - ~T- In Pdi,,o~
P"....
(-
RT
F i n ( [K]° exp \
+
2RT
/
(22)
+ [Na]o exp (-c + B~r~))
\ (A~2RT
The new Equation (16) or (22) is thus a counterpart of the original Nernst
equation. While the latter describes the potential difference between two
similar ionic phases (both dilute solutions) the present equation deals with
the potential difference at an interphase separating two similar o r different
phases. Several interesting features of Equation (16) may be mentioned.
(a) It shows that a fixed charge system ~ o u g h it strongly adsorbs its counterions may nevertheless give rise to a potential at the surface separating the
fixed charge phase and another phase.
(b) The potential is related to the concentration of the surface-fixed anionic
charges, If-I, and not to the macroscopic bulk phase K + ion concentration,
although under certain conditions they may be proportional or even the
same. A single homogeneous intracellular ionic concentration is a corollary
of the membrane theory not shared by the fixed charge-induction hypothesis
according to which both the density and the c value of the fixed charges may
vary from one microscopic area to another within the same cell. For this
reason the lack of correlation between ~b and [K] i, which directly contradicts
the membrane potential theory, is in accord with the fixed charge-induction
hypothesis.
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AE~ = A~c + B,,
Published May 1, 1960
x62
PHYSIOLOGY
OF CELL
MEMBRANE
(c) T h e equation has the same form of Equation (1 I) after excluding the
C1- term.
(d) T h e potential is determined by the critical parameter, the c value. As
we shall presently illustrate, a small variation in this parameter alone can
create a profound change of the potential such as that observed when a resting
muscle or nerve becomes excited.
Equation (22) can be written in the form
RF
~
-=
ln[J-]
a~x
+
~-
R T in Pa..oo
F
Pdi,.oo
-- ~F~ In ( [K]o -t- [Na]° exp ( A x - AN.)e2RT
+ (Bx -- B . . )
)
(23)
At the resting c value, of - 2 . 7 .~, from Fig. 3, we find
(A,r -- AN,)c q- (BK -- BN.)
2RT
Equation (23) is reduced to
~/, =
-- --
F
in ~
+
~
+
In [K]surtace
(24)
[K]o
Pdi~o0
Since almost all the surface anions are now occupied by K + ions the equation
simplifies to
= - ~ m ~
ai,~oo
+
+
In
[K]o
(25)
If the surface-fixed charge density and c value and other characteristics are
such that [K]surta. m a y approach the value of [K];
= const +
[K],
In [K]o
(26)
which is the original Nernst equation. This accounts for the occasionally
observed correlation between ~ and the gross intracellular K + ion concentration in ceils (e.g., high potential and high [K]~ in living cells, low potential
and [K]¢ in dead ceils, see also Desmedt, 1953). Since the ~f-] m a y have no
direct correlation with [K]~ at all we also encounter the disparities mentioned
earlier. N o w if the surface-fixed anionic charges have the same average
density as those in the bulk phase of muscle ~f-] should be about 150 raM/
liter (see monograph). ( R T ) / ( F ) In (~-])/([K]o) at [K]o - 2.5 n ~ / l i t e r
would be approximately 100 my. or 2.5 kcal./mole. F r o m Fig. 3 AE~:/2
at the c value of --2.7 ~ is about --6 kcal./mole. Since ~ actually measured
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[K]o >> [Na]o exp
Published May 1, 1960
L~o SelectiveIonicPermeabilityand CellularPotentials
163
is some 100 millivolts or 2.5 kcal./mole ( R T ) / F In (PA°°oo)/(Pdi,,°o) approximates --6.0 kcal./mole which gives (Pai,~o,)/(P~,°~) = 2.2 X 104, a not
unreasonable figure.
Since the potential is determined only by events at a microscopic surface
we m a y expect any new equilibrium potentials to be reached instantaneously
(see below). Thus if we bring about an abrupt c value shift of the surface sites
by the indirect F process, the change of potential is represented by Equation
(22). Let us say this c value shift leads to a new value of - 2 . 1 /~. Rewriting
Equation (22) i n the form
AE.N.
~k =
RT
In[f-'] + T
Pu, oo
F In Pdi.soe
(27)
, R T I n / [ N a ] ° + [K]o exp ( A s . - A~c + ( B N . - Br.)~
F
[
"
2RT
I
[Na], >> [K]° exp
(As,, -- Ar.)c + (Bs,
2R T
- -
BK)
We arrive at the following equation
~=_RffZlnP~,~o
A~,
Pai..o~ + -W- +
~_Tln ~- ]
[Na]o
(28)
Now [Na]o in frog Ringer solution is about 100 rr~/liter. If-] is 150 raM/liter.
(RT)/(F) In ([f-])/([Na]o) is then 10 my. or 0.2 kcal./mole. We have already
calculated (RT)/(F) In (P~,,,oo)/(Pdi,,oo) to be - 6 . 0 kcal./mole. At c -- --2.1
~,/2
-- - 8 kcal./mole. F r o m Equation (28) one calculates ~ = - 90 my.
A small shift of c value equal to six-tenths of an /:'kngstrom unit will thus
create a reversed potential of some 100 inv. with the intracellular phase
positive. I n neurophysiology this is known as the "overshoot" (Curtis and Cole,
1942; Hodgkin and Huxley 1952a; 1952b).
Experimental Evidence in Support o[ the Present Model of Cellular
Potentials
Having shown how the fixed charge system can possess a surface potential
and yet retain most of its accumulated countercations within the bulk phase
in an adsorbed form, we next turn to two physical systems that have for some
time been considered as typical models demonstrating m e m b r a n e potentials
as given by the Nernst equation (for earlier abstracts see Ling, 1955b; 1959).
In the glass p H electrode the glass m e m b r a n e has been supposed to be
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and at this new c value
Published May 1, 1960
164
PHYSIOLOGY
OF CELL MEMBRANE
selectively permeable to H + ion and impermeable to, say, K + ion. In apparent
agreement the potential can be shown to follow the equation
RT, a~
~b --- --if- m---~
(29)
ao
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in which a~ refers to the H + ion activity inside the glass bulb, usually as that
of a 0 . 1 N H C l , and ao~"is the activity of H + ion in the outside solution. While
this is the conventional view, not all workers in this field agree on this concept.
Thus Horovitz (1923) and H a u g a a r d (1941) have offered convincing evidence that the potential measured above is really an algebraic sum of two
surface potentials. T o this category of contradictory evidence against the
m e m b r a n e concept we can also add the not uncommon practice of filling the
inside bulb not with a 0.1 N HC1 b u t with mercury or simply coating it with
a layer of metal. In these eases a perfectly usable H + ion measuring glass electrode is obtained (Thompson, 1932; H u b b a r d and Rynder, 1948) while
there is no m e m b r a n e equilibrium to speak of at all.
A second model also long accepted as a model of the living cell m e m b r a n e
is the collodion membrane. Michaelis and coworkers have demonstrated
that such a m e m b r a n e is capable of giving a nearly ideal potential when it
separates two aqueous solutions containing different K + ion concentrations.
In other experiments Michaelis was actually able to demonstrate selective
permeability through such membranes to such ions as K + and N a +. These
experiments served as an important foundation on which the m e m b r a n e
potential theory was built (Michaelis and Fujita, 1925; Michaelis and
Perlzweig, 1926-27). In view of our knowledge of the glass electrode one
wonders if the potential measured in the collodion m e m b r a n e m a y not be the
same as in the glass electrode, simply representing the algebraic sum of two
surface potentials. In that case selective ionic permeability would be a phenomenon related to the potential but not, as the m e m b r a n e theory suggests,
the cause of it.
T o put this to a test the author and Mr. L. Kushnir have chosen a C o m i n g
015 soft glass bulb which is known to be sensitive to H + but not to K + ion.
Fig. 4 Shows this K + insensitivity. T h e solid line with solid circles represents
the potential measured while the outside K+ ion concentration varied. T h e
dashed line with empty circles shows a similar curve when the K + ion concentration inside the glass bulb was varied. N o w a thin layer of dried collodion
measuring no more than 3# in thickness was applied onto the surface of the
glass bulb and the potential again measured against a varying external K +
ion concentration. This curve is shown as a dashed line with solid circles.
Within the range of K + ion concentrations, 1 to 100 m~, a change of 54 milli-
Published May 1, 1960
LINo
Selective Ionic Permeability and Cellular Potentials
t65
volts was measured for each ten-fold change of [K] 0; this is identical with that
which we measured on a simple dried collodion membrane electrode. 4
N o w as mentioned earlier the glass electrode has no sensitivity toward K +
ion at all. According to the membrane theory this must be interpreted as
proof of the impermeability of the glass bulb toward the K + ion. Similarly,
in terms of the membrane theory one must interpret the demonstrated K + ion
sensitivity of dried or wet collodion as due to a high K + ion permeability. In
the combination membrane used, the glass component is a great deal thicker
*Jaan the collodion component. The over-all permeability must therefore be
150
/
.,o
s, f
.I
fl
I00
f~
50
I
f
/
J
/
/
,¢
/
0
*
/
•
..- . .
m
-"
---
outside soln, voried
inside soln. voried
glass electrode
collodion electrode
°,.
-50
f
0
I
I
t
t
2
!
I
3
I
4
-Log rK ÷]
F1ouP.~ 4. Effect of varying K + ion concentration on the electrical potential. T h e solid
line with solid circles and the dash line with empty circles represent measurement made
on glass surfaces. T h e dash line with solid circles represents measurements made on
collodion-coated (3/z) glass electrodes.
very low toward K + ion. Yet this combination membrane demonstrated
exactly as great a sensitivity toward K + ion as the simple collodion membrane
itself. It is a long established fact that pure collodion does not give rise to
potentials and that only after it has acquired fixed carboxyl groups either as a
result of incidental or deliberate oxidation does it develop the electrode
behavior (Sollner, Abrams, and Carr, 1941). The conclusion is reached
that the potential is determined only by the nature and density of the fixed
charges on the surface of a fixed charge system and bears only an indirect
4 In other experiments virtually the same results were obtained when,the collodion coat was not
dried but used while still wet. Yet it is known that wet and dried collodion have totally different
gross permeabilities toward ions (see Michaelis and Perlzweig, 1926-27).
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E
f
Published May 1, 1960
z66
PHYSIOLOGY
OF
CELL
MEMBRANE
relation to the gross permeability of ions through the m e m b r a n e which separates the inside solution from the outside solution in such systems. While the
above experiment shows that the potential of glass and of dried collodion does
not depend upon the gross permeability of these membranes these conclusions
are only directly applicable to these particular models. Next we shall present
an experiment dealing not with models of living cells but with the living cells
directly. T h e result of this experiment seems once again incompatible with
the m e m b r a n e theory of cellular potential but strongly suggests the explanation offered by the present hypothesis.
According to the fixed charge-induction hypothesis the resting potential of
a frog muscle fiber, as in other cells, is a partial expression of an equilibrium
I00
\
3 0 uM K °
60
40'
20:
¢,
HOURS
Fxotrt~ 5. The time course of change of the resting potential of a frog sartorius muscle
in a Ringer solution containing 105 mM of sodium and 30 mu of potassium (pH, 7.4)
at room temperature measured with a microelectrodc.
state existing between the K + ions in the external solution and the K + i o n s
adsorbed on the fixed anions of a superficial surface layer of the cell. Thus
variation in the external K + ion concentration should lead to an almost instantaneous readjustment of the equilibrium at this surface. Paralleling this
there would be an almost instantaneous change to a new stable and unvarying
resting potential. T h e time course of change of the resting potential is thus
expected to be independent of the change of gross intraceUular K + ion concentration while the m e m b r a n e theory demands that they run parallel
courses.
Fig. 5 shows the results of an experiment in which a frog sartorius muscle
resting in a Ringer solution containing 2.5 m M K + is suddenly plunged into a
Ringer solution containing 30 nlM K + and a normal amount of N a + (pH 7.4).
Within the time required to make the firstmeasurement, the resting potential
dropped to a new equilibrium value from which there was no significant
deviation over 10 hours later. The effect of such an increase of external K +
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80 ¸
Published May 1, 1960
Lmc
Selective Ionic Permeability and Cellular Potentials
x67
SELECTIVE IONIC PERMEABILITY
In a fixed charge system the fixed charge and counterion pair occupy definite
locations. At the average charge density found in practically all living tissues
the electrostatic field owing to the fixed charges and their counterions are
very high. Recalling that owing to the dielectric saturation phenomena the
dielectric constant of water between a pair of closely placed cation and anion
is considerably below the macroscopic value of 8 I, a simple calculation shows
that the potential at the weakest point is of the order of magnitude of 200 inv.
Continuous energy barriers thus exist that effectively bar the entry of external
ions through the interstices of the fixed charge system (Fig. 6). The majority
of ions thus must seek a different route in entering the ceils. According to the
fixed charge induction hypothesis the most likely one is by associating with
the fixed charge of opposite sign on the surface after successfully displacing
another counterion originally occupying the site. For the entry of K 4' ions
into muscle cells:
K 4'
KeF -+X
+
F--.K
~
~
Ka.--F-'-.K
Ku . - . F - . - . X
~
~
KaF "
+
K
(30)
F - X + aKi4]+ (1 -- a)Ko%~ (31)
Thus it takes two steps for an external K a to enter into the cell: a first suc-
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ion concentration on the intracellular concentration of K + is available. It is
well established that in such a high K + concentration, t h e [K]~ of frog sartorius muscle will steadily rise approaching an equilibrium in 6 to 10 hours
(room temperature) with a half-time of equilibrium at about ½ to 2 hours
(Fenn and Cobb, 1934; Conway, 1946; Harris, 1952). Equation (1) or (11)
predicts a gradual and continual rise of the measured potential within this
length of time until the new equilibrium [K]~ was reached. That the total
potential change is achieved immediately and that once it is established does
not further change demonstrates once more the inadequacy of the membrane
theory. The same experiment also rules out the possibility of a sizeable
potential at the diffusion front of the inward migrating excess K + ion (see
also footnote 4). For if it existed, it would have died out at about 10 hours at
which time the new equilibrium [K]~ would be reached. With this the diffusion potential should vanish after following a steady declining time course.
None of this was observed. This leaves only the macroscopic surface of the
living cell as the site at which the potential is generated as suggested in
Equation (16). Experimentally this is in perfect accord with the instantaneous
assumption of a new equilibrium value on changing [K], and the observation
that the potential in model glass and collodion electrode likewise depends
only on the nature of the fixed charges immediately contiguous to the external
solution.
Published May 1, 1960
150
~10o
E
50
_
0
0.1
0,2
53
I/S ~mM-I)
0.4
0.5
F m U ~ 7. The effect of varying of the external Rb + ion concentration (0, 4, and 25
n~/liter) upon the initial rate of entry of K + ion into muscle (sartorius, semitendinosus,
tibialis anticus and ileofibularis muscles of frog). K ~ was used as a tracer. The experiment was performed at 0°C. (pH 7.4).
168
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FIGURE 6, Diagrammatic illustration of the electric potential fields near the surface
of a fixed charge system. Each line represents a more or less permanent isopotential
line. The diagram demomtrates the continuous energy barriers toward the entry of
cations and aniom through the "meshes."
Published May 1, 1960
Lmo
Selective Ionic Permeability and Cellular Potentials
t69
20
O
15
~o
s
0
K
~
2
4
6
8
~Csl
~0~
~K
to
Fmums 9. The effect of varying the external
K + ion concentration on the rate of entry of
CsTM (the value for KC1 concentrations are to
be multiplied by 4 trm/liter) into sulfonate
exchange resin sheets, Nalfilm-1. The Cs
concentrations are in tertm of number of
counts per cubic centimeter. The rates of
entry are in terms of counts per minute per one
arbitrary unit surface. (25°C. pH 7.0-7.1).
cessful occupation of a surface-fixed charge and a second successful displacement by another cation X. 6
W h e n there is another cation, say Rb +, present with K ~2 in the bathing
solution both will compete for the same limited number of fixed charges on
s While we have discussed this series of events as if it were only on the surface of the fixed charge
system actually it occurs throughout the whole bulk phase of the fixed charge system. What is dis'
cussed here as permeability is thus strictly speaking a diffusion phenomenon.
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F m u ~ 8. The effect of varying the external K + ion concentration (0, 20, 30 raM/liter)
upon the initial rate of entry of Rb + ion into frog mnscle using RbSS as tracer. 0°C. pH
7.4.
Published May 1, 1960
I70
PHYSIOLOGY
OF CELL
MEMBRANE
the cell surface. Based on these assumptions one can derive from Langmuir's
adsorption isotherm an equation analogous to that of Michaelis-Menten
derived for the competitive inhibition in enzyme action
I
I I
r[Rb]o]
= ,,-;w
+
(3z)
1
in which the reciprocal of the rate of K 4~ entry, VK'' plotted against the reciprocal of the concentration of K 4~ [K ~] o in the presence of varying concentration of the interfering ion [Rb] o, should give a family of rectilinear curves. I f
all of these should converge toward the same locus on the ordinate the analysis
m
6
4
2
0
...............
0
I
I ....
I
I
I
2
3
4
5
6
I/[ Cs*]
Fmtra~ I0. The effect of varying the external K+ ion concentration (units of concentration same as in Fig. 9) on the rate of C~m entry into oxidized collodion membrano. The rates of entry are in terms of counts per unit surface. This unit surface is
defined by the lucite rods of identical dimensions on which the collodion membranes
were east (25°(:]. pH 7.0-7.1).
indicates that there is a competitive adsorption at a specific site before entry
can occur. T h e equilibrium constant of the fixed charge for K+ ion, Kx,
and for R b + ion, Kab, can also be derived from these curves.
Epstein in 1952 first brilliantly applied this analysis to the rate of entry of
R b + Ca+, and K+ ions into barley roots (1952). Parts of the results of a study
of the entry of R b +, Cs + and K + ion into frog muscles were reported by Ling
Downloaded from on June 18, 2017
..>
Published May 1, 1960
Lmo
SelectiveIonic Permeability and Cellular Potentials
I71
(1953; 1954; 1955) and are reproduced in Figs. 7 and 8. s In 1958 Conway
and Duggan made similar studies of ionic entry into yeast (Conway and
Duggan, 1958). Both Epstein, and Conway and Duggan, however, regarded
the competitive nature thus demonstrated as a verification of the concept of
active transport, according to which, ions have to combine with a postulated
2.0
,
/
°
50 KCI
i.6
-
5 KCI
I KCI
0
v
...>
0.8
0.4
0.0
I ,
o
o.1
I
I
[
I
0.2
0.3
0.4
0.5
o
I/[Cs*]
Fmtrmz 11. The effect of variation of external K + ion concentration (units of KCI
concentration etc. same as in Fig. 9) on the rate of CsTM entry into 0.03 gm. of
scoured, defatted virgin sheep's wool (25°C. p H 7.0-7.1).
carrier to enter into the cells. The shortcomings of this model have been discussed by the present author (1955a). Perhaps it might be mentioned that
the carrier theory could be greatly strengthened if an experimental model can
be found to demonstrate its operation.
6 Harris and Sjodin (1959) published in abstract the results of similar experiments which verify these
results on frog muscle. These authors were apparently unaware of our earlier work.
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1.2
Published May 1, 1960
172
PHYSIOLOGY
OF CELL
MEMBRANE
The major work involved in the theoreticalcalculationsand in the reported studieson ionic entries
into frog muscles wcrc aided by a grant from the Muscular Dystrophy Associationsof America, Inc.
while the author was on the facultyof the Department of Psychiatry,University of Illinois,Chicago,
during the years 1954 to 1957.
The author is indebted to Mrs. M a r y Carol Williams and Mrs. Margaret Samucls for their
invaluable help in the theoreticalcomputations; to Miss. Arlene Schmolinskc for her assistancein
the experimental work on ion permeability of frog muscles; to Mr. Leo Kushnir, the coauthor of a
few forthcoming papers from which some of the presented data have bccn taken. Finally the author
takes pleasure expressing his thanks to his student and colleague, Dr. Samuel B. Horowitz, for his
assistancein preparing the manuscript and for his valuable criticismand discussion;to Mrs. Betty
Jane Brcuckcr for typing the manuscript.
The author takes pleasureacknowledging the generous giftof sheep'swool from J. IArcbb and Son
Co., Inc., Philadelphia, and Hcmphill and Co., Inc., Philadelphia.
REFERENCES
AsTauaY, W. T., Ann. Rev. Biochem., 1939, 8, 113.
BERNSTEm,J., Arch. ges. Physiol., 1902, 92, 521.
Bjp.aatn% N., If. Dan. Vid. Selsk., 1926, 7, No. 9.
BRANCH, G. E. K., AnD CALvn~, M., The Theory of Organic Chemistry, New York,
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BUNOENBERODE JONQ, H. G., in Colloid Science, (H. R. Kruyt, editor), Amsterdam,
Elsevier Publishing Co., Inc., 1949, II, 287.
CONWAV,E. J., Nature, 1946, 157, 715.
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On the other hand, there are numerous fixed charge systems that we encounter daily. The present hypothesis demands that if a system has a sufficient number of fixed charges on its surface and in its bulk then the same competitive nature of ionic entry should be the rule. To put this postulation to
the test we have chosen three well-established fixed charge systems (Ling and
Kushnir, data to be published).
(a) A sulfonate exchange resin of the polymerized polystyrene-divinylbenzene type bearing fixed sulfonate groups.
(b) An oxidized dried collodion membrane long established to contain a
large n u m b e r of fixed earboxyl groups (Sollner et aL, 1941).
(c) Wool which is a pure protein. According to the fixed charge-induction
hypothesis its glutamic acid and aspartic acid residues (at a concentration
of about 800 mM/kg.) should provide a large number of fixed anionic charges.
The studies of the entry of Cs 184into each of these fixed charge systems in
the presence of varying amount of K + ion were made and the results shown
for sulfonate exchange resin in Fig. 9, for dried collodion in Fig. 10, and for
sheep wool in Fig. 11. All unequivocally show the same type of competitive
ionic entry as occurs in living cells. Since w e cannot imagine the exchange
resin, the dried collodion or the sheep wool to possess ionic carriers or pumps,
the kinetics observed must arise from the nature of fixed charge systems itself.
Published May 1, 1960
LI~o SelectiveIonic Permeability and Cellular Potentials
173
Downloaded from on June 18, 2017
CONWAY, E. J., AND DUOGAN,F., Biochem. J., 1958, 69, 265.
COWAN, S. L., Prec. Roy. Soc. London Series B, 1934, 115,216.
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DEAN, R., Biol. Syrup., 1941, 3,331.
DEB','S, P., AND HiiCKEL, E., Physik. Z., 1923, 24, 185.
DSMEDT, J. E., J. Physiol., 1953, 121, 191.
DONNAN, F. G., Z. Elektrochem., 1911, 17,572.
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EISENMAN, G., RtmIN, D. O., AND CAS]3Y,J. U., Paper presented at the 10th annual
Conference on Electrical Techniques in Medicine and Biology of the A.I.E.E.,
I.S.A., and I.R.E., Boston, November, 1957, not printed.
EPSTF.XN,E., Plant Physiol., 1952, 27,457.
FALK, G., AND GERARD, I~. W., J. Cell. and Comp. Physiol., 1954, 43, 393.
FENN, W., AND COBB, D., J. Gen. Physiol., 1934, 17,629.
FOWLER, R. H., AND GUOGENn~XM,E. A., Statistical Thermodynamics, Cambridge
University Press, 1939.
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