Membrane Potential
Introductory article
Article Contents
Keith S Elmslie, Tulane University School of Medicine, New Orleans, Louisiana, USA
. Introduction
A thin lipid bilayer membrane with embedded proteins surrounds all cells. The potential
difference across this membrane depends on the ionic concentrations on either side of this
membrane and the permeability of the membrane to those ions.
. Resting Membrane Potential: A Characteristic of All
Living Cells
. Action Potentials: A Characteristic of Excitable Cells
. Electrical Signals Produced by Ionic Movement Across
the Plasma Membrane: The Roles of Channels and
Pumps
Introduction
If you were to place a sensitive electrical measuring device
in the extracellular solution (surrounding a cell) you would
find no change in voltage as you moved the device (an
electrode) through this solution. If you made small
injections of current through the electrode you would find
that there was very little resistance to the electrical current
in this solution. This means that the ions in the solution
(sodium (Na 1 ), potassium (K 1 ), calcium (Ca2 1 ) and
chloride (Cl 2 )) are free to move throughout the solution
(no impediments). When, on the other hand, this electrode
is placed into a cell, you measure a decrease in voltage of
60 mV. Thus, the inside of a cell is 2 60 mV compared to
the outside of the cell. If you now made small current
injections, you would find a high resistance. The cell’s
membrane resists the movement of ions, which is one factor
resulting in the potential difference across the cell
membrane. However, the membrane is not completely
impermeable to ions. (If that were the case, the potential
difference across the membrane would be zero.) A class of
proteins called ion channels form passages through the
membrane. A small number of ions diffuse across the
membrane generating the membrane potential that can be
measured by the electrode. Ion channels can be selective for
particular ions and they can be regulated. Thus, the cell can
control the passage of ions across its membrane by
controlling the activity of ion channels. The two forces
that control the movement of ions through the open
channels are concentration and electrical forces. The
concentration force is generated by a class of proteins
called ion pumps that use cellular energy (adenosine
triphosphate, ATP) to establish differential ion concentrations across the membrane. The electrical force is
established by the ion selectivity of the membrane,
allowing positively charged ions to leave the cell but
trapping negatively charged ions inside the cell. Together
these forces drive ions through the open channels, creating
the membrane potential. (see Cell membranes: intracellular pH
and electrochemical potential.) (see Ion channel biochemistry.)
. Single-ion Electrochemical Equilibrium: The Nernst
Equation
. Multi-ion Electrochemical Equilibrium: The Goldman
Equation
. High Resting Permeability to Potassium and the
Membrane Potential
. Summary
Resting Membrane Potential: A
Characteristic of All Living Cells
The net movement of molecules in a solution depends on
the concentration gradient. Molecules move from areas of
high concentration to areas of low concentration by the
process of diffusion (Figure 1a). If a pathway is provided
across the cell membrane, the net direction of the movement of a molecule can be predicted by the difference in the
concentration. For example, urea is a compound that can
move through the membrane (it is membrane permeant). If
we place a cell that contains no urea into a solution
containing 1 mmol L 2 1 urea, urea will diffuse into the cell
(down its concentration gradient) until the cellular
concentration of urea equals 1 mmol L 2 1. (For simplicity
we assume the volume of the cell is small relative to that of
the bath, so the concentration of urea in the bath does not
change.) At equilibrium (when the concentration is
equalized) urea still crosses the membrane, but the movement into the cell equals the movement out of the cell; that
is, the net movement of urea is zero at equilibrium. Thus,
concentration gradients form a chemical force directing the
net movement of molecules. All living cells maintain
differential ion concentrations across the cell membrane so
that the concentration of each ion is larger on one side of
the membrane than the other. Table 1 lists the main
physiological ions for a typical mammalian neuron,
together with their intracellular and extracellular concentrations. While these values are for a neuron, similar ion
concentrations are found for other cells. Note that the
concentration difference is not the same for each ion; for
example, the potassium (K 1 ) concentration is higher on
the inside of the cell, while the sodium (Na 1 ) concentration is higher outside the cell. Since membrane is permeable
to K 1 and Na 1 , the chemical force will drive these ions to
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1
Membrane Potential
Time = infinity
(equilibrium)
Time = zero
Zero
mmol L–1 urea
1 mmol
L–1 urea
Chemical force
1 mmol
L–1 urea
1mmol
L–1 urea
Chemical force
= zero
(a)
Time = infinity
(equilibrium)
Time = zero
Em = 0mV
100mmol
L–1 K+
100mmol
L–1 Cl–
Chemical force
10mmol L–1 K+
Electrical force
= zero
10mmol L–1 Cl–
Chemical force
Em = –58mV
100 mmol
L–1 K+
10mmol L–1 K+
Electrical force
100 mmol
L–1 Cl–
10 mmol L–1 Cl–
(b)
Figure 1 The forces that control the movement of molecules across the
cell membrane. (a) Chemical forces control the movement of nonionic
molecules across the membrane. At time zero a cell is placed into a bath
containing 1 mmol L 2 1 urea. The concentration gradient across the
membrane is initially large, which creates a large chemical force to move
urea into the cell. At equilibrium, the concentration of urea is equal across
the membrane and the chemical force has dropped to zero. The two
headed arrow indicates that the urea still crosses the membrane, but at
equilibrium efflux equals influx. (b) In this example, the cell membrane is
permeable to K 1 , but not Cl 2 . At time zero, the cell containing 100 mmol
L 2 1 KCl is placed into a bath containing 10 mmol L 2 1 KCl. Initially, the
concentration gradient generates a concentration force that drives K 1 out
of the cell. With time (a few milliseconds), a negative potential is created
inside the cell by the Cl 2 left behind by K 1 efflux. This build-up of negative
charge creates an electrical force that pulls K 1 back into the cell. At
equilibrium the negative membrane potential generates an electrical force
that exactly balances the chemical force. Thus, the net K 1 flux (summation
of inward and outward flux) equals zero. Note that, unlike urea, the
concentration of K 1 is virtually unchanged between the initial conditions
and equilibrium. This is because only a small number of K 1 ions need to
cross the membrane to generate a voltage large enough to balance the
chemical force.
diffuse down their concentration gradients. In order to
maintain the gradients, the cell must expend energy in the
form of ATP to pump the ions against their concentration
gradient. (see ATPases: ion-motive.)
The movement of urea and other uncharged molecules is
controlled by the concentration gradient; however, electrical forces together with chemical forces control the
movement of ions. To illustrate the electrical force, let us
assume a cell containing 100 mmol L 2 1 KCl is placed into
a solution of 10 mmol L 2 1 KCl, but the membrane is only
permeant to K 1 (Figure 1b). As K 1 begins to diffuse from
the cell down its concentration gradient, Cl 2 is left behind,
as it cannot diffuse across the membrane. Thus, as K 1
leaves the cell a negative potential is established across the
membrane (because of the build-up of negative Cl 2 ions
inside the cell). Opposite electrical charges attract, so the
negative potential is a force that ‘pulls’ the K 1 back into
the cell. Note that in the case of K 1 the electrical and
chemical forces oppose each other in a resting cell
(membrane potential (Em) 5 2 60 mV). The chemical
force drives K 1 out of the cell, while the electrical forces
drive K 1 into the cell. K 1 will leave the cell (making the
membrane more negative) until the electrical force
becomes large enough to balance the chemical force. The
potential at which this balance is achieved is called the
equilibrium potential. The electrical and chemical forces
together are termed the electrochemical force or gradient.
Differential ion concentration is one of the factors
needed to generate the resting membrane potential
(typically between 2 60 and 2 100 mV); however, no
potential can develop if the membrane is equally permeable
to all ions. The other factor in generating a membrane
potential is the selective permeability of the membrane. At
rest, the membrane is selectively permeable to K 1 . Thus,
the resting membrane potential of all cells is sensitive to the
K 1 gradient. If the extracellular K 1 concentration is
raised without altering the intracellular K 1 concentration,
the membrane potential is brought closer to zero (depolarized). Scientists studying the effect of membrane potential
on cellular physiology and/or biochemistry often manipulate the extracellular K 1 concentration to alter the
membrane potential. Equations presented below allow
calculation of the membrane potential based on the ion
concentration when only a single ion is permeant. When
Table 1 Concentrations of some ions outside and inside a mammalian neuron
Ion
1
K
Na 1
Cl 2
Ca2 1
A2
[Outside] (mmol L 2 1)
[Inside] (mmol L 2 1)
Ex (mV)
5
150
125
2
–
150
15
9
0.0001
108
2 86
+58
2 66
+250
N/A
Values obtained from Hille (1992), Ganong (1997) and Matthews (1991). The equilibrium
potentials (Ex) are calculated for room temperature of 208C. These Ex values would
increase by a factor of 1.06 for body temperature (378C). A 2 represents membrane
impermeant organic anions (primarily proteins, amino acids and phosphate ions).
Because these anions do not cross the membrane, they do not have an equilibrium
potential. N/A, not applicable.
2
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Membrane Potential
the membrane is permeable to multiple ions, a second
equation will be presented that considers both the ion
concentrations and the relative membrane permeability in
the calculation of membrane potential.
Cells use differential ion concentrations (and the
resulting membrane potential) for many important functions. As we will see below, excitable cells (nerve and
muscle cells) use the membrane potential for electrical
signalling. However, nonexcitable cells (the majority of
cells in the body) use the force generated by the
electrochemical gradient to aid in the transport of essential
substances across the cell membrane. In each case, the
energy of the ion gradient of one ion (typically Na 1 ) is
used to move a second molecule. For example, amino acids
are transported into the cell via the Na 1 –amino acid
cotransporter protein. The concentration of amino acids is
higher inside the cell and so energy must be used to move
them against their concentration gradient. The cotransporter binds the amino acid and Na 1 simultaneously and
uses the energy of the Na 1 electrochemical gradient to
power the movement into the cell. Another example of this
type of transport is called the Na 1 /Ca2 1 exchanger,
because Na 1 and Ca2 1 are moved in opposite directions.
The intracellular concentration of calcium (Ca2 1 ) is
maintained at a very low level ( 100 nmol L 2 1) by the
cells. This is compared to an extracellular concentration of
2 mmol L 2 1. As with Na 1 , both the electrical and
chemical forces favour the movement of Ca2 1 into the cell.
However, Ca2 1 is an important cellular messenger and
increases in the intracellular concentration of Ca2 1 are
therefore used to signal events. For this reason, random
increases in intracellular Ca2 1 must be opposed, and
signalling-induced increases must be rectified. One of the
mechanisms the cell uses to maintain low intracellular
Ca2 1 concentration is the Na 1 /Ca2 1 exchanger. This
protein uses the electrochemical Na 1 gradient to transport
Ca2 1 out of the cell. Thus, the electrochemical forces
created by the ion gradient and selective membrane
permeability play very important roles in cell physiology.
(see Transport of small molecules.) (see Ion transport across
nonexcitable membranes.) (see Calcium signalling and regulation
of cell function.)
Action Potentials: A Characteristic of
Excitable Cells
All cells have a resting membrane potential, but only
excitable cells use the membrane potential to generate
signals. The two types of electrical signals are receptor
potentials and action potentials. Receptor potentials are
generated in sensory nerve terminals in response to sensory
stimulation and in postsynaptic cells in response to
activation of receptor/ion channels by neurotransmitters.
These potentials travel (or propagate) passively along the
membrane. Passive propagation means that these potentials decay exponentially with distance from their starting
point. Action potentials, on the other hand, are actively
propagated along the membrane. This is accomplished by
action potentials being sequentially induced in each small
patch of membrane as they move along. The ionic
mechanisms involved in the generation and propagation
of the action potential is described elsewhere. Briefly, the
action potential involves a transient influx of Na 1 that
depolarizes the membrane to nearly 1 40 mV. This is
followed by a K 1 efflux that rapidly returns the membrane
to its resting level. The propagation occurs because the
Na 1 influx at one membrane patch leads to the
depolarization and the subsequent Na 1 influx in the next
patch. (see Action potential: generation and propagation.)
The action potential is the mechanism by which
information is transmitted within most neurons in the
nervous system (some neurons in the retina and ear use
only receptor potentials). The important property of the
action potential is that it can be transmitted long distances
without alteration. This is extremely important because the
axon extending from a single neuron can be over 1 metre
long (e.g. sensory neurons that have axons extending from
the tip of the toes to the base of the brain). The information
carried by action potentials is accurately transmitted over
these vast distances. (see Action potential: ionic mechanisms.)
Electrical Signals Produced by Ionic
Movement Across the Plasma
Membrane: The Roles of Channels and
Pumps
Under physiological conditions, the membrane bilayer is
impermeant to ions. The lipids that comprise the membrane are hydrophobic (dislike water), while ions are
hydrophilic (like water). Thus, the ions will remain in the
water and avoid the hydrophobic membrane. The ions
cross the membrane via a class of transmembrane proteins
called ion channels (Figure 2). These proteins form waterfilled pores through the membrane that provide the
pathway for ions to move in response to the electrochemical forces. One class of ion channels passes cations
(positively charged ions) and the other class passes anions
(namely Cl 2 ). Within the cation class there exist ion
channels that are nonspecific, in that they pass cations
without strongly selecting between them. More commonly,
ion channels are selective in that they will primarily pass a
single ion, such as Na 1 , K 1 or Ca2 1 . These ion channels
are named according to their primary permeant ion (i.e.
Na 1 channels, K 1 channels and Ca2 1 channels). (see Lipid
bilayers.) (see Ion channels.) (see Sodium, calcium and potassium
channels.)
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3
Membrane Potential
Extracellular
solution
Plasma
membrane
Cytoplasm
(a)
required because the ions are transported across the
membrane against their concentration gradients. The most
important of these pumps is the Na 1 /K 1 ATPase (also
called the Na 1 /K 1 pump). This protein simultaneously
transports (or ‘pumps’) Na 1 out of the cell and K 1 into
the cell. The Na 1 /K 1 ATPase is the reason for the
differential concentrations of Na 1 and K 1 across the cell
membrane (Table 1). Thus, the ‘leak’ channels establish the
resting membrane potential by allowing Na 1 and K 1 to
cross the membrane, while the Na 1 /K 1 ATPase maintains the differential ion concentrations. (see Potassium
channel diversity: functional consequences.) (see Adenosine triphosphate.)
Single-ion Electrochemical Equilibrium:
The Nernst Equation
ADP + Pi
ATP
(b)
Figure 2 Ion channels and pumps move ions across the plasma
membrane. (a) Ion channels form water-filled pores that permit the
hydrophilic ions to pass through the hydrophobic lipid bilayer membrane.
The direction of ion flux through the open channel is governed by
electrochemical forces. (b) Ion pumps move ions by using energy from ATP
hydrolysis. In this cartoon the pump will simultaneously transport two
different ions in opposite directions (analogous to the Na 1 /K 1 ATPase).
The pumps move the ions against their concentration gradients. In other
words, the ions are moved from an area of low concentration to an area of
high concentration. From left to right: ions bind to sites in the pump (left).
This binding triggers the hydrolysis of ATP (middle), which alters the
conformation of the pump to release the ions on the opposite side of the
membrane (right). Once the ions are released the pump returns to its
resting position, ready to bind and transport more ions.
The role of the ion channels is to set the permeability of
the membrane. The majority of those that are involved in
setting the resting membrane potential are permeable to
K 1 . A smaller number are permeable to Na 1 . These ion
channels are often called ‘leak’ channels because they are
always slowly ‘leaking’ K 1 and Na 1 ions to maintain a
stable resting membrane potential. However, the activity
of these channels would result in the loss of the ionic
gradients across the cell membrane if it were not for the ion
pumps, a class of proteins that use energy to move ions
across the membrane. One type of pump described above
was the Na 1 /Ca2 1 pump, which used the energy of the
Na 1 gradient to move Ca2 1 out of the cell. Unlike the
Na 1 /Ca2 1 pump, the ion pump that maintains the Na 1
and K 1 gradients utilizes the energy derived from ATP
hydrolysis to power the movement of ions. This energy is
4
As stated above, the resting membrane potential is
primarily controlled by the K 1 concentration across the
cell membrane. Thus, as a first approximation, we can
model the membrane of a resting cell as being exclusively
permeable to K 1 . This simplification will allow us to
explore the relationship between the chemical and electrical forces discussed above. Specifically, for a given
concentration gradient across the membrane, we can
calculate the membrane potential at which the electrical
and chemical forces are balanced. This potential is called
the equilibrium potential. To illustrate this, consider the
example in Figure 1b where a cell containing 100 mmol L 2 1
KCl is placed into a solution of 10 mmol L 2 1 KCl, and the
membrane is selectively permeable only to K 1 . At the
equlibrium potential the K 1 influx driven by electrical
force is equal to K 1 efflux driven by the chemical force.
The equilibrium potential can be calculated from the ion
concentrations across the membrane using the Nernst
equation: (see Nernst, Walther Hermann.)
Ex ¼
RT
½Xo
ln
zF
½Xi
½1
where X is the ion in question (K 1 in this example), R is the
gas constant (8.315 J K 2 1 mol 2 1), T is the temperature in
degrees Kelvin, z is the valence of ion X (z 5 1 1 for K 1 )
and F is Faraday’s constant (9.648 104 C mol 2 1). Below
is an example calculation using the K 1 concentrations
from Figure 1 and a room temperature of 208C,
Ex ¼
8:315 J K1 mol1 293 K
½10 mmol L1 o
ln
1
½100 mmol L1 i
þ1 9:648 104 C mol
which reduces to EK 5 2 0.0583 J C 2 1. Since 1 J (joule) 5 1 V C (volt coulomb), EK 5 2 58.3 mV.
In biology we generally work with a simplified form of
the Nernst equation where room temperature is 208C and
the natural log (ln) has been transformed into log10. This
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Membrane Potential
(E 5 IR) can be used to relate current with driving force
and conductance:
form of the equation is:
Ex ¼
½Xo
58 mV
log
z
½Xi
Ix 5 Gx (Em 2 Ex)
½2
It may be surprising that we are using initial conditions to
calculate an equilibrium voltage. Indeed, it is clear that ions
must cross the membrane to create a voltage. If ions are
crossing the membrane, how can we use initial concentrations in this calculation? To answer this question, we need
to know how many ions need to cross the membrane to
achieve the equilibrium potential. Based on the electrical
properties of the cell membrane, it can be calculated that
only approximately one billionth of the total number of
K 1 ions need to cross the membrane in order to achieve
the equilibrium potential. Since the net movement of only a
small number of ions is required to counter a large
concentration force, it is valid to use the initial concentrations to calculate the equilibrium potential.
The K 1 concentrations illustrated in Figure 1 were used
to simplify the calculation of the equilibrium potential. As
can be seen in Table 1, the K 1 concentration inside the cell
is higher than in our example, and the concentration
outside is lower. This results in the K 1 equilibrium
potential of a real neuron being hyperpolarized to that we
calculated in our example ( 2 86 mV versus 2 58 mV). In
addition to K 1 , an equilibrium potential can be calculated
for each permeant ion (Table 1). Note that Na 1 ions are
more concentrated in the extracellular solution compared
to the cytoplasm, which results in a positive equilibrium
potential. Thus, unlike K 1 , at resting membrane potential
both the chemical force and the electrical force are directed
inward for Na 1 .
Because the equilibrium potential is the voltage at which
ion influx and efflux are balanced, when the membrane
potential deviates from the equilibrium potential
those ions move in a direction that will return the
membrane potential to the equilibrium potential. For
example, if the membrane potential is set to 2 40 mV, K 1
will flow out of the cell in order to hyperpolarize the
membrane to EK ( 2 58 mV in the example of Figure 1). On
the other hand, if the membrane potential is 2 80 mV, K 1
will flow into the cell to depolarize the membrane
to EK. Thus, with a constant concentration gradient the
ion flux is directly proportional to the difference between
the membrane potential (Em) and the equilibrium potential
for that ion (Ex). This difference is called driving force
and is formally written Em 2 Ex. Driving force dictates the
direction of ion flux, while the magnitude of ion flux is
determined by the driving force and the membrane
permeability to that ion. One way to describe membrane
permeability is as the conductance of the membrane to
an ion (Gx), which is the ease with which an ion will
cross the membrane. Ion flux can be measured as ionic
current (I, in coulombs per second, C s 2 1). Ohm’s law
[3]
where Gx 5 1/Rx (resistance) and E 5 driving force
(Em 2 Ex).
Multi-ion Electrochemical Equilibrium:
The Goldman Equation
The single ion example nicely illustrates the forces on ion
movement, but real cells have multiple permeant ions.
Using the Nernst equation, we can calculate the equilibrium potential for each ion, but with multiple permeant
ions the membrane potential is no longer equal to the
equilibrium potential of a single ion. In order to calculate
the membrane potential, we need to know the relative
membrane permeability of each ion. This can be illustrated
using Figure 3a, which shows the ion gradients for Na 1 and
K 1 for a typical mammalian cell. The equilibrium
potentials under these conditions are 2 86 mV and
1 58 mV for K 1 and Na 1 , respectively. Thus, in the
extreme situation, if the membrane were exclusively
permeant to K 1 the membrane potential would be
2 86 mV. Alternatively, if the membrane were exclusively
permeant to Na 1 , the membrane potential would be
1 58 mV. Of course, this never happens. In reality the cell
membrane is simultaneously permeant to several ions.
Thus, the membrane potential is related to the relative
permeability of the membrane to the permeant ions. For
example, if the membrane were equally permeable to Na 1
and K 1 the membrane potential would be the average of
ENa and EK, which is 2 14 mV. In a multi-ion system, we
need to know the equilibrium potential for each permeant
ion and the membrane permeability for each ion before we
can calculate the membrane potential (Em). This relationship can be quantified using the Goldman equation, which
is also called the constant field equation:
RT
pK ½Kþ o þ pNa ½Naþ o þ pCl ½Cl i
ln
½4
F
pK ½Kþ i þ pNa ½Naþ i þ pCl ½Cl o
where pX is the permeability of ion X and R, T and F have
the same meaning as in the Nernst equation. Note that the
intracellular and extracellular Cl 2 concentrations are
reversed from those of Na 1 and K 1 . This is done to keep
the sign positive, since ln (A/B) 5 2 ln (B/A). In the
Goldman equation, each concentration term is scaled by its
permeability. This demonstrates that an ion cannot
contribute to the membrane potential if its membrane
permeability is zero.
It is much easier to experimentally measure relative
permeability than actual permeability. In such a case,
permeability is usually expressed in reference to the
Em ¼
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5
Membrane Potential
Em = EK = –86 mV
Em = ENa = +58 mV
150 mmol L–1 K+
5 mmol L–1 K+
150 mmol L–1 K+
5 mmol L–1 K+
15 mmol L–1 Na+
150 mmol L–1 Na+
15 mmol L–1 Na+
150 mmol L–1 Na+
9 mmol L–1 Cl–
125 mmol L–1 Cl–
9 mmol L–1 Cl–
125 mmol L–1 Cl–
(a)
Em = ? mV
Na+–K+ pump
150 mmol L–1 K+
K+ 5 mmol L–1
15 mmol L–1 Na+
Na+ 150 mmol L–1
9 mmol L–1 Cl–
Cl– 125 mmol L–1
108 mmol L–1 A–
(b)
Figure 3 Relative permeability of ions determines the membrane potential for a given set of ion concentrations. (a) Two examples where either K 1 (left)
or Na 1 (right) is the only permeant ion. In each case, the membrane potential equals the equilibrium potential for the permeant ion. (b) In a real cell the
membrane is permeable to K 1 , Na 1 and Cl 2 . The Goldman equation is required to determine the membrane potential, as it considers both the ion
concentrations across the membrane and the permeability of each ion.
potassium permeability. Therefore, the Goldman equation
typically takes the form of:
Em ¼
½Kþ þ b½Naþ o þ c½Cl i
RT
ln þ o
F
½K i þ b½Naþ i þ c½Cl o
½5
where b 5 pNa/pK and c 5 pCl/pK. The equation can be
further simplified by removing Cl 2 . This simplification is
valid in neurons because the Cl 2 conductance is small
relative to that of potassium and contributes little to resting
membrane potential. However, such simplification is not
appropriate for other cells, like skeletal muscle cells, where
resting Cl 2 conductance is high. This simplified form of
the Goldman equation is:
Em ¼
½Kþ þ b½Naþ o
RT
ln þ o
F
½K i þ b½Naþ i
½6
where b has the same meaning as in eqn [5]. Note that the
equation can be further simplified by converting the
natural log (ln) into the log10 and using room temperature
to convert RT/F to 58 mV. If one is to use this form of the
Goldman equation (eqn [6]) in research, it is up to the
investigator to verify that pCl/pK ratio is negligible and that
Cl 2 contributes little to membrane potential.
6
High Resting Permeability to Potassium
and the Membrane Potential
The simplified form of the Goldman equation allows us to
explore the relative permeabilities of Na 1 and K 1 in
relationship to the membrane potential. Using the ion
concentrations of Table 1, we can calculate a Em of
2 62 mV if the membrane were 20 times more permeable to
K 1 than Na 1 (b 5 0.05). This value is close to that for a
neuron at rest. Therefore, we conclude that a neuron at rest
is 20 times more permeable to K 1 than to Na 1 . On the
other hand, if the membrane were 20 times more permeable
to Na 1 than K 1 (b 5 20), Em would equal 1 48 mV,
which is close to the peak of the action potential. From this
we can conclude that at the peak of the action potential the
Na 1 conductance is 20 times larger than that of K 1 .
This change in the relative permeability of the membrane
to Na 1 occurs as a result of the activation of voltage
dependent Na 1 channels. The activation of these channels
is transient, but the resulting depolarization activates
voltage-dependent K 1 channels, which help return
(repolarize) the membrane to the resting potential.
(see Sodium channels.) (see Voltage-gated potassium channels.)
In the example in Figure 1, Cl 2 was membrane
impermeant. Recall that this was the source of the negative
charge remaining in the cell which resulted in the electrical
force that ‘pulled’ K 1 back into the cell. However, the
Goldman equation has a Cl 2 permeability term. In
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Membrane Potential
addition, it was stated above that Cl 2 permeability is quite
high in some cells (e.g. skeletal muscle cells). Yet these cells
maintain an electrochemical force as strong as the cells with
little Cl 2 permeability. How can the negative internal
potential develop if the membrane is permeable to Cl 2 ? In
real cells, a diverse group of organic molecules that cannot
readily cross the membrane function as impermeant anions
(Table 1, Figure 3). This group of anions, referred to as A 2 in
Table 1, includes proteins, charged amino acids (glutamate
and aspartate) and phosphate ions.
In a cell with multiple permeant ions the membrane
potential does not equal the equilibrium potential for any
ion. Therefore, ions will move across the membrane in an
effort to drive the membrane potential to their respective
equilibrium potentials. Without intervention the ionic
gradients would decline with time, resulting in a loss of
membrane potential. As discussed above, ion pumps
prevent the loss of the ionic gradient. The Na 1 /K 1
ATPase maintains the Na 1 and K 1 gradient, but it also
contributes to the membrane potential. This contribution
comes from this protein moving 3 Na 1 out of the cell for
every 2 K 1 it transports into the cell. This 3 : 2 ratio means
that the pump generates a negative current as it works and
this current has been shown to hyperpolarize the cell
membrane. In one study, the Na 1 /K 1 pump was shown
to contribute 10 mV to the resting membrane potential.
In the absence of the pump (blocked using a drug called
oubain), the resting membrane potential averaged
2 65 mV. However, the resting potential was 2 75 mV
with the pump working.
Summary
The regulation of selective ion channels allows the cell to
set the permeability of its membrane to inorganic ions. The
permeability of the membrane is one factor involved in
setting the membrane potential. A second factor is the
gradient of ion concentrations across the membrane. This
gradient is established by ion pumps that use the energy of
ATP hydrolysis to move ions from areas of low concentration to areas of high concentration. For each permeant ion
we can calculate the membrane potential at which the
chemical and electrical forces are balanced so that the net
flux of that ion is zero. Intracellular impermeant anions,
together with the concentration gradient and relatively
high K 1 permeability, establish a resting membrane
potential where the inside of the cell is 60 mV negative
to the outside. Excitable cells (e.g. neurons) have voltagedependent ion channels that are selective for Na 1 and K 1 .
Activation of the Na 1 channels depolarizes the membrane
towards the Na 1 equilibrium potential. Subsequent
activation of voltage-dependent K 1 channels returns the
membrane to its resting potential.
Further Reading
Ganong WF (1997) Review of Medical Physiology, 18th edn. Stamford,
CN: Appleton and Lange.
Hille B (1992) Ionic Channels of Excitable Membranes, 2nd edn.
Sunderland, MA: Sinauer.
Levitan IB and Kaczmarek LK (1997) The Neuron: Cell and Molecular
Biology, 2nd edn. New York: Oxford University Press.
Matthews GG (1991) Cellular Physiology of Nerve and Muscle, 2nd edn.
Boston, MA: Blackwell Scientific.
ENCYCLOPEDIA OF LIFE SCIENCES / & 2001 Nature Publishing Group / www.els.net
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