A M . ZOOLOCIST 10:347-354 (1970).
The Origin of Bioelectrical Potentials in Plant and Animal Cells
JOHN GCTKNECHT
Department of Physiology and Pharmacology, Duke University Medical Center,
Durham, N. C. 27706, and Duke University Marine Laboratory,
Beaufort, N. C. 28516
SYNOPSIS. The electrical potential difference across a plant or animal cell membrane can
be caused by at least three different mechanisms, acting alone or in concert. First, a
Donnan equilibrium can account for a sizable membrane potential without the participation of any active transport process. In a Donnan equilibrium the membrane potential is generated by the diffusion of permeating ions down their concentration gradients. The asymmetric distribution of permeating ions is caused by the presence of
charged, nondiffusible ions, e.g., proteins inside the cell. The second mechanism is an
electrically neutral ion pump, e.g., the coupled sodium-potassium pump found in many
types of cells. An electrically neutral pump can generate a large membrane potential if
the membrane has a high passive permeability to one of the actively transported ions,
usually potassium. The third mechanism is an electrogenic ion pump, which makes a
substantial contribution to the membrane potential in several types of plant and animal cells. An electrogenic pump directly causes a net movement of charge across the
cell membrane. The membrane voltage generated by the pump then causes a passive
How of diffusible ions which partially short circuits the potential difference generated
by the pump.
A striking feature of all living cells is the
difference in electrical potential which exists between intracellular and extracellular
fluids. This potential difference usually
ranges from 10 to 100 millivolts, with the
inside of the cell electrically negative to
the outside. Bioelectrical potentials can be
both the cause and the result of ionic
transport processes. Therefore, any attempt to understand electrolyte transport
and metabolism in living cells must include a knowledge of the voltage difference
across the cell surface. A biologist attempting to solve a problem involving the
transport of electrolytes often finds that
obtaining and interpreting bioelectrical
data is the most difficult aspect of his problem. Therefore, in this article I shall discuss briefly the measurement and applications and, in somewhat more detail, the
origins of bioelectrical potentials in plant
and animal cells.
First we will consider the physical meaning of a bioelectrical potential. The existence of a steady potential difference across
the surface of a cell implies a separation
of positive and negative charges. This
means that the numbers of positive and
negative charges inside a living cell are not
exactly equal. This may appear to be a
contradiction of the electroneutrality rule
which we use often in physical-chemical
calculations. The contradiction is only microscopic, however, as the following example will show. The actual amount of
charge (q) which must be separated to
give rise to a bioelectrical potential can be
estimated from a knowledge of the voltage
difference (say, —100 mv) and the capacitance of a biological membrane (about
10 -(i farads/cm2).
q = c v s (10-° farads/cm2) (10-' volts)
s= 10~7 coulombs/cm2
Dividing by the Faraday (ca. 105 coul/equiv) gives 10~12 equiv/cm2. If we are
dealing with the interior of a spherical cell
20 microns in diameter, then the negative
charges will outnumber the positive charges
by about 10- c equiv/liter. This concentration difference is negligible compared to the actual concentration of electrolytes in a living cell, so that on a macroscopic, but not microscopic, scale the assumption of electroneutrality still holds.
With regard to the physical location of
347
348
JOHN GUTKNECHT
the potential difference in a living cell, the
potential drop must occur almost entirely
across the outer plasma membrane (plasmalemma). This statement is based on the
fact that the specific resistivity of cytoplasm is low (about 10 ohm-cm) compared to the specific resistivity of the plasmalemma (106-1010 ohm-cm). Therefore,
every point within the cytoplasm must be
at a similar potential. In plant cells this
argument applies also to the relation between the vacuolar membrane (tonoplast)
and the vacuolar contents (sap). Other
membrane-bounded organelles, e.g., mitochondria and nuclei, also maintain internal potentials which differ from the potential of their cytoplasmic environment.
Because of the high electrical resistance of
the microelectrode circuit (106-108 ohms),
the apparatus must be carefully grounded
and shielded to reduce electrical interference (see Suckling, 1961).
Penetration of the cell surface with a
microelectrode must be accomplished with
a minimum of damage. Otherwise the potential difference will be partially short
circuited by electrical leaks around the site
of puncture. Thus, membrane potential
measurements require, in addition to finetipped microelectrodes, micromanipulators
and special holding devices which vary
with the type of cell being studied (Kopac, 1964). In general, the ease with which
a membrane potential can be measured is
roughly proportional to the size of the cell
being studied. Thus, intracellular potenMETHODS OF MEASURING B1OELECTRICAL POtials were measured in giant algal cells
TENTIALS
(Osterhout, 1931) more than 20 years beIn this article we will consider only the fore comparable data were obtained from
measurement of "resting" membrane poten- ordinary-sized cells, e.g., muscle 100 p diatials rather than the measurement of tran- meter (Ling and Gerard, 1949). More resient (time-dependent) potentials which oc- cently, membrane potentials have been
cur in excitable cells. Resting membrane measured in cells as small as 8-12 /* diamepotentials are usually measured by contact- ter, e.g., Chlorella (Barber, 1968) and red
ing the interior of a cell with a microelec- blood cells (Lassen and Sten-Knudsen,
trode (strictly speaking, a micro salt 1968; Jay and Burton, 1969). Finally,
bridge). The microelectrode is usually a fine membrane potentials have also been reglass capillary, less than 1 micron tip di- corded from nuclei (Lowenstein and Kanameter, filled with a concentrated KC1 solu- no, 1963) and mitochondria (Tupper and
tion (see Frank and Becker, 1964). The Tedeschi, 1969).
KCl-filled microelectrode makes contact via
Having successfully impaled a living
a KCl-agar bridge with a KCl-calomel elec- cell, we will record a potential difference
trode, which converts ionic current into which is the algebraic sum of several poelectrical current. The calomel electrode is tentials (see Dainty, 1962). These are (1)
connected to a voltmeter which has suffici- the potentials which may occur in the unently high input resistance (>1010 ohms) stirred layers of solution on either side of
so that the amount of current drawn by the membrane; (2) the liquid junction pothe voltmeter will not affect the membrane tentials at the tips of the salt bridges, and
potential we wish to measure. The circuit (3) the potential difference across the cell
is completed by another KCl-calomel membrane, which is the potential we wish
electrode which makes contact with the to know. The potentials arising from unexternal solution via another KCl-agar stirred layer effects are negligible when a
bridge. The complete circuit, in its sim- cell is in a steady state, i.e., when influxes
plest form, is therefore
and effluxes of ions are identical. The liquid junction potential at the tip of a micell
microKC1
calomel
croelectrode filled with 3 M KC1 should, in
membrane cytoplasm electrode bridge electrode
principle, be small, because the mobilities
calomel
KC1
external
of K and Cl in aqueous solution are nearvoltmeter electrode bridge
solution
349
ORIGIN OF BIOELECTRICAL POTENTIALS
ly equal. However, the microelectrode tip
can easily become charged by the adsorption of proteins or other polyvalent ions,
and, if so, the transport numbers of K and
Cl may no longer be similar and a large
junction potential may arise at the tip of
the microelectrode (Adrian, 1956). This
"tip potential" may be subtracted from
the membrane potential provided it is reasonably small and stable. Certainly a necessary (but not always sufficient) criterion
for an acceptable measurement of a membrane potential is that the tip potential
before impalement be the same as the tip
potential after the microelectrode is withdrawn from the cell.
From this brief introduction it should be
clear that the measurement of bioelectrical potentials requires a combination of
physical, chemical, and biological techniques. Frank and Becker (1964) provide a
comprehensive discussion of microelectrode techniques, including the construction, filling and storage of various types of
glass capillary electrodes. An introduction
to bioelcctricity and bioelectronics is
provided by Suckling (1961). For a general review of physical and chemical principles see Gordon and Woodbury (1965),
Spanner (1964), and Glasstone and Lewis
(1963). For earlier reviews on bioelectrical
potentials see Crane (1950) and Ridge
and Walker (1963).
Tl-IEORICIN OF BIOELECTRIC POTENTIALS
The Donnan Equilibrium
If two electrolyte solutions are separated
by a membrane through which one or
more of the ionic components cannot pass,
a Donnan equilibrium will be set up.
This Donnan equilibrium is characterized
by an unequal distribution of ions and a
difference in the osmotic pressure, hydrostatic pressure, and electrical potential
of the two solutions. The possible importance of Donnan equilibria in biological
systems is suggested by the existence of
differences in electrolyte concentrations,
osmotic pressure, hydrostatic pressure, and
electrical potential of intracellular and extracellular fluids. The Donnan equilibrium
is discussed in detail by Overbeek (1956)
and Spanner (1964). Here we will use a
simplified and practical approach in attempting to answer the question: To what
extent can a Donnan equilibrium, explain
the electrical, ionic, and osmotic relations
which we find in living cells?
All plant and animal cells contain substantial amounts of nondiffusible electrolytes, chiefly proteins, to which the plasmalemma is virtually impermeable. The
presence of these nondiffusible, but osmotically active, proteins make the living cell
an unstable system which will tend to swell
due to an osmotic flow of water into the
cell (see Dainty, 1962; Tosteson, 1964).
Most plants and microorganisms have, in
addition to a semipermeable plasmalemma, a cell wall which acts as a mechanical
barrier to osmotic swelling and allows the
development of a hydrostatic (turgor)
pressure within the cell. A walled cell thus
provides a convenient starting point for
assessing the role of the Donnan equilibrium in living cells.
Consider a bacterial cell suspended in
dilute saline containing Na, K, and Cl
(Fig. 1A). This hypothetical cell contains
Na, K, Cl, water, and dissolved protein, A~
(100 mM/liter, valence = —1). Both the
cell membrane and the cell wall are permeable to Na, K, Cl, and water, but the
cell membrane is impermeable to protein.
The cell membrane has no capacity for
active transport of solutes or water, and so
a Donnan equilibrium exists. We will now
calculate the intracellular ionic concentraK = 8mM
Cl = 62 mM
A'=l00mM
P= 3Ootmos
E m =-I2mv
A
K = 5mM
• Cl =IOOmM
= IO5mM
Cl = 5mM
A" =100 mM
AP • O.2otmos
= -78mv
B
FIG. 1. Doimaii equilibria in two hypothetical microorganisms. The cells are encompassed by a plasma membrane and a cell wall. Cell A is impermeable only lo protein, A", whereas cell B is impermeable to both protein and Na.
JOHN GUTKNECHT
350
tions, osmotic pressure, hydrostatic pressure, and electrical potential. Then we will
compare these values with the values we
might expect to find in a real microorganism.
Because Na, K, and Cl are in electrochemical equilibrium, we can use the
Nernst equation, derived in the preceeding
article by Koch, to calculate the relations
between the ionic concentration differences
and the membrane potential.
Em =
(1)
Ej
RT
—
CjO
In
59
=
Cj°
log
millivolts
where Ein is the membrane potential
(mv), Ej is the equilibrium potential for
each ion (Na, K, and Cl), Cj° and C/ are
the concentrations of each ion outside and
inside, Zj is the ionic valence, and R, T,
and F have their usual meanings. (We
have made the usual approximation that
the activity coefficients are similar for ions
in the cytoplasm and in the external solution). From the Nernst equation for each
ion we get the Donnan ratios for the diffusible ions, i.e.,
(Na°) (Cl°) = (Nai) (Cl1)
(2)
(K?) (Cl«) = (K<) (Cl<).
(3)
and
Adding equations (2) and (3) gives
Cl° (Na»+K«) = Cl! (Na' + Ki).
(4)
Alacroscopic electroncutrality requires that
the sums of the positive and negative
charges in each phase be zero. Therefore,
(5)
and
l' = Na'-J-Ki.
(6)
Substituting from (5) and (6) into (4) gives
or
(7)
Inserting the numerical values of Cl° and
A' into equation (7) and solving the
quadratic equation for Cl' yields Cl' = 62
mM. Inserting the Cl concentration ratio
(100/62) into the Nernst equation (1)
gives Em = —12 mv, and from the Donnan
ratios we find that Na' = 154 mM and K
= 8 mAf. The difference in osmotic pressure, from van't Hoff's equation, is
n'—77° = R T (N;ii-(-Ki + Cl i +
Ai—Na°—K.»—Cl°)
= 3.0 atmos
(8)
which is also the difference in hydrostatic
pressure at equilibrium, i.e., the hydrostatic pressure sufficient to raise the chemical
potential of water inside to the value ol
that outside.
Note that the presence of charged intraccllular protein has two important consequences. First, the charge on the protein
is responsible, indirectly, for the potential
difference. The direct cause of the potential difference is, of course, the charge separation which occurs as Na, K, and Cl tend
to diffuse down their concentration gradients. But if the net charge on the intraccllular protein were zero, then at equilibrium the concentration gradients for diffusible ions would also be zero and the membrane potential would be zero. The second
important effect of the charge on the cytoplasmic protein is that it causes the sum of
the Na, K, and Cl concentrations to be
higher inside than outside. This means
that the excess osmotic pressure inside is
due in part to the dissolved protein per se
and in part to the effect of the protein's
charge on the equilibrium distribution of
ions.
The values we have calculated for E,n,
Air, Nao/Na*, KyK1, and CiyCl 1 in our
hypothetical microorganism
(Fig. 1A)
are, in fact, fairly close to the values found
for E. coli in the stationary phase
(Schultz, et ah, 1962). Thus, the Donnan
equilibrium is apparently a reasonable
starting point for understanding the electrical, osmotic, and ionic relations of living
cells. However, most cells maintain a
larger potential difference and a higher
ratio of K:Na inside than can be accounted for by a simple Donnan equilibrium. Furthermore, most animal cells are
ORIGIN OF BIOELECTRICAL POTENTIALS
isosrnotic to their environment, i.e., the hydrostatic pressures inside and outside are
similar. These three features, i.e., a large
membrane potential, a high intracellular
ratio of K:Na, and a small difference in
hydrostatic pressure can be achieved by
adding one additional restriction to our
Donnan system. That is, we can specify
that the cell membrane be impermeable to
Na as well as to protein. Repeating the
previous calculations with the additional
assumption that neither protein nor Na
can cross the cell membrane yields the values shown in Figure IB. Although the values obtained are perhaps more lifelike,
our assumption about sodium impermeability is unrealistic. Exposure of living cells
to radioactive sodium invariably shows
that Na does cross the cell membrane at a
slow, but finite, rate. Thus in the steady
state, low intracellular Na cannot be accounted for by an impermeability of the
plasmalemma to Na. To explain completely the ionic relations of most living cells
we must, therefore, look beyond the Donnan equilibrium.
Electrically Neutral Ion Pumps
Because the Donnan equilibrium cannot
account for some important features of
the ionic and electrical properties of living
cells, we must look for other mechanisms,
which means, of course, active transport of
solutes and/or water. In this section we
will consider one of the hypotheses about
active transport and membrane potentials
which has been popular for the past 10-15
years. This hypothesis says that the plasmalemma contains a metabolic transport
system for Na and K which is capable of
moving both these ions uphill, i.e., from
regions of lower to higher electrochemical
potential. This Na and K transport is
mediated by a single transport system
which shifts its affinity from Na to K on
opposite sides of the membrane, so that the
outward movement of Na is coupled to an
inward movement of K. This coupled NaK pump was first proposed in erythrocytes
to explain the approximately equal and
351
opposite transports of Na and K, as well as
the fact that extrusion of Na requires the
presence of external K (see Whittam,
1964). Implicit in the hypothesis of a coupled Na-K pump is the idea that it is
electrically neutral. That is, the coupled
pump makes no direct contribution to the
membrane potential because one positive
charge is extruded for each positive charge
brought in.
At first, it may seem that an electrically
neutral pump cannot be responsible for a
large potential difference across the cell
membrane. This might be true if the cell
membrane had no additional selective permeability properties. However, most cell
membranes discriminate sharply between
Na and K, and so the large differences in
concentrations created by the Na-K pump
can and do generate large membrane potentials. Usually the cell membrane is
much more permeable to K than to Na, so
the membrane potential is close to, but
less than, the equilibrium potential for K.
(If EK and Em were equal, then the inward
and outward leaks of K would be equal
and the Na-K pump would cause a net
influx of K until a new steady state was
attained.)
If the membrane is permeable to several
ions, e.g., Na, K, and Cl, then Eln will be a
function of the permeabilities and concentration differences for all these ions.
This can be stated mathematically by the
Goldman or constant field equation, which
is derived in the preceding paper.
Em=
RT
(9)
In-
PKKo+PNaNa°-f-PclCli
PKK*-|-PNaNa'+PclClo
The Goldman equation says that the membrane potential is the result of asymmetric
distributions of passively moving ions
which have differing mobilities in the
membrane. An implicit assumption in the
Goldman equation is that the ion pump is
electrically neutral. This means that if the
ion pump were stopped by a specific inhibitor, there would be no immediate change
in the membrane potential, although the
352
JOHN GUTKNECHT
potential would slowly run down as the
ionic asymmetries were abolished. In some
cells this seems to hold true, thus supporting the hypothesis of an electrically neutral pump. However, some other cells behave as though the membrane potential is
more closely coupled to the active transport system itself.
Electrogenic Ion Pumps
Until recently ion jDumps were generally
thought to be electrically neutral. However, in principle, there is no reason why an
ion transport system cannot cause a net
movement of charge and thus make a direct and immediate contribution to the
membrane potential. This type of ion
pump is described as electrogenic. There is
now a growing body of evidence that ionic transport processes in some plant and
animal cells can be electrogenic (see
Keynes, 1969). The unequivocal demonstration of an electrogenic pump is not an easy
task, mainly because various combinations
of membrane permeabilities often prevent
the electrogenic pump from greatly influencing the membrane potential. For example, if the membrane resistance is low (i.e.,
if the membrane is leaky to some ion),
then the voltage generated by an electrogenic pump will be largely short-circuited
by the passive ionic flux.
Perhaps the most thoroughly investigated electrogenic pump is the Na-K
pump in several types of nerve and muscle. Apparently in these cells the coupling
ratio of Na-extrusion to K-absorption can
be greater than one. For example, in the
giant cell of the gastro-esophageal ganglion of Anisodoris, a marine mollusc, the
resting membrane potential is separable
into two distinct components (Marmor
and Gorman, 1970). One component
shows a classical dependence on ionic gradients and ionic permeabilities. This component of the membrane potential is accurately described by the Goldman equation (9). A second component of the
membrane potential depends directly on
metabolic activity, i.e., on the Na-K pump.
This second component is abolished by
ouabain, low temperature, low internal
Na, and low external K, all of which are
thought to inhibit the Na-K pump. Only
when the Na-K pump is inhibited can the
membrane potential be described accurately by the Goldman equation. The obvious
interpretation of these results is that the
ratio of Na extruded to K absorbed is
greater than unity, which allows the Na-K
pump to make a direct contribution to the
membrane potential.
In plant cells the clearest example of an
electrogenic pump is the Cl-influx pump
in the marine alga, Acetabularia (Saddler,
1970a, b). In Acetabularia the normal resting potential is —170 mv. Low temperature, darkness, CCCP (an uncoupler of
photophosphorylation), and low external
Cl all rapidly depolarize the membrane
by about 90 mv and simultaneously reduce
the active influx of Cl to a low level.
These four conditions do not affect the
efflux of Na or K, thus ruling out the
possibility that an electrogenic cationic
efflux contributes to the potential. The potential difference remaining after inhibition of the Cl-influx pump (about —80
mv) is primarily a K-diffusion potential,
which can be described by the Goldman
equation (9). This ionic diffusion potential is completely independent of the electrogenic component. Thus, simple addition
of the diffusional and electrogenic components can account for the whole potential under all conditions.
APPLICATION OF BIOELECTRICAL POTENTIALS
TO
TRANSPORT PROBLEMS
One of the first things we wish to know
when studying electrolyte transport and
metabolism is: Which ions are moving passively and which ions are actively transported across the cell surface? Active transport processes are usually identified by exclusion, i.e., active transport can be denned
as a flow of ions which does not conform
to expected passive behavior. In this section 1 will describe one simple way of ex-
ORIGIN OF BIOELECTRICAL POTENTIALS
pressing quantitatively this deviation from
passive behavior.
One clear way to demonstrate active
transport is to show a net uphill movement
of ions, i.e., a movement from a region of
lower to higher electrochemical potential.
Net uphill transport clearly requires a
minimum expenditure of metabolic energy
which is equal to the rate of net transport
times the electrochemical potential difference, fj—fn,0. However, cells as we find
them in their normal environment are
usually in a steady state. That is, the
influxes and effluxes of ions are generally
similar. The problem then is to identify
the ions which are in a steady state but
which are not in electrochemical equilibrium.
In the steady state the extent to which
an ion departs from electrochemical equilibrium can be estimated by comparing the
calculated equilibrium (Nernst) potential,
Ej, with the measured membrane potential, Em. This comparison is based on the
following derivation. The difference between the electrochemical potentials of an
ion inside and outside a cell is
w'-rt° = (RT In
(10)
(RT In
= zjF(Ei—E°)—RT In
therefore, the direction of active transport.
For example, in the marine alga, Valonia ventricosa, the influx and efflux of K
are normally about equal, i.e., 80-90 X
10- 12 moles/cm2sec. The K; is about 625
mM, compared with a K° of about 12
mM. Thus the equilibrium potential for
K, from equation (1), is about —102 mv,
compared with a measured potential of -|-17
mv. Thus, Em — EK = -f 121 mv or, multiplying by zK F, about 1.2 X 104 joules/mole. The large and positive value of Em —
EK tells us that there is a large outward
driving force acting on the cation K, and
therefore the passive efflux must be much
larger than the passive influx. In other
words, a large part of the K-influx must be
active (see Gutknecht and Dainty, 1968).
Of course, the smaller the value of Em —
Ej, the less compelling is the evidence for
active transport, because there are unavoidable sources of error in the measurement of Em and Ej, as well as in the measurement of ionic fluxes. Finally, this
method of identifying actively transported
ions is only one of several conventional
methods. Additional criteria for active
transport are discussed in other articles of
this series.
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where E' — E°— E,n, the actual membrane
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Oj/C'j = Zj F Ej, where Ej is the equilibrium potential for the ion j , i.e., the potential difference that will balance the observed difference in concentration for a
particular ion. Substituting from equation
(1) into equation (9) gives
W«-JIJo = z J F(E n -E J )
353
(11)
Thus, under steady-state conditions the
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E^ (joules/mole or calories/mole) tells
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