Adv Physiol Educ 40: 543–547, 2016;
doi:10.1152/advan.00049.2016.
Illuminations
An intuitive approach to understanding the resting membrane potential
David Cardozo
Department of Neurobiology, Harvard Medical School, Boston, Massachusetts
Submitted 4 April 2016; accepted in final form 18 October 2016
Address for reprint requests and other correspondence: Dept. of Neurobiology, Harvard Medical School, 220 Longwood Ave., Boston, MA 02115
(e-mail: [email protected]).
cating this idea to college undergraduates and even high school
students. The essence of the approach is to regard establishing
Vm as an engineering problem by imagining a cell building its
membrane potential stepwise, using only simple principles
familiar to all high school graduates. The first step toward
understanding Vm is to discuss the foundational principles
(Table 1). Students are typically very comfortable with these
ideas and find them intuitive.
The first two assumptions state that, through random motion,
ions move independently and diffuse down their concentration
gradients. Students intuitively understand that random collision
will lead to this form of diffusion. From these ideas, we can
demonstrate that diffusion is an energy source and that the
amount of work that can be done is proportional to the log of
the concentration gradient (Fig. 1A). To establish a concentration gradient across the membrane, the cell utilizes the Na⫹/K⫹
ATPase, which pumps K⫹ into the cell and Na⫹ out, thereby
establishing concentration gradients for the two ions. This
ATP-dependent pump is involved in active transport of the two
ions against their concentration gradients. It moves 3 Na⫹ out
and 2 K⫹ in with each pump cycle. The maintenance of the
gradients is energetically very expensive, and it is estimated
that approximately one-third of the brain’s metabolism is
dedicated to supplying ATP in support of this process. K⫹ is
high inside and low outside, and the situation for Na⫹ is just
the reverse. Although concentration gradients are established
for different ion species before establishment of Vm, there are
equal concentrations of total ions inside and outside of the cell
and every positive ion is accompanied by a negative partner,
resulting in charge neutrality.
We focus on K⫹, which has an approximately 140:4 inside/
outside ratio (see Fig. 5) and has channels that are open in the
resting state. The magnitude of this concentration gradient is
illustrated in Fig. 1B. We note that through random motion
there will be many more collisions on the inside of the
membrane than on the outside. When a channel permeable to
K⫹ is placed in the membrane, the more frequent random
collisions on the inside membrane surface (Fig. 2A) will result
in a net exit of K⫹ ions through the channel (Fig. 2B). This is
an energy source. Imagine a paddle wheel placed inside the
channel. The greater number of collisions from the exiting ions
will cause the wheel to turn in one direction (Fig. 2C). If one
imagines the paddle wheel connected to a coil spring, then with
each turn of the wheel the spring will be compressed and
energy will be stored. The amount of work that can be done as
a result of diffusional energy is Wd/mole ⫽ RT ln (Cin /Cout). As
mentioned above, the equation states that the amount of energy
is a function of the steepness of the concentration gradient.
This is an idea that students find intuitive. Slightly more
sophisticated students can appreciate that it takes the form of a
differential equation representing a case in which the rate of
change is a function of the size of the concentration gradient.
1043-4046/16 Copyright © 2016 The American Physiological Society
543
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A FUNDAMENTAL PROPERTY OF CELLS is that through the use of ion
transporters they maintain intracellular ion concentrations that
differ from those of the extracellular environment (15). Although it is not known precisely how this difference in ion
concentrations came about in evolution, numerous studies
indicate that the intracellular ion concentrations of cells likely
reflect the extracellular conditions at the time when the first
cells arose. It is hypothesized that the earliest cells (or protocells) had leaky membranes and evolved in habitats with high
K⫹/Na⫹ ratios and relatively high concentrations of the Zn2⫹,
Mn2⫹, and phosphates. These early environments may have
been ocean hydrothermal vents or inland geothermal systems.
In either case, migration of the early cells to the high Na⫹ and
low K⫹ conditions of the ocean required ion-impermeable
membranes, ion-selective channels, and ion pumps capable of
maintaining the gradients. Evolution took advantage of the
large disparity between internal and external K⫹ and utilized it
as a source for a resting membrane potential (4, 10, 13, 14).
The existence of K⫹-specific ion channels in the membranes
of virtually all cells results in a membrane potential (Vm)
across the cell membrane, making the inside of the cell electrically negative relative to the extracellular solution. In addition, certain classes of cells, notably neurons and muscle cells,
also have voltage-sensitive Na⫹ channels in their membranes,
rendering these cells excitable. Opening of the Na⫹ channels
results in an influx of positive Na⫹ ions (known as the action
potential), resulting in a transient change of Vm from its
negative resting state to positive potential. This mechanism is
at the heart of neuronal signaling and muscle contraction (9).
One of the most difficult concepts for students to master is
a logical and intuitive understanding of how an ionic gradient
can be utilized to establish an electrical potential difference
across a biological membrane. In my experience, dealing with
students at all levels, from high school through medical school,
the vast majority never master this concept. The electrical
potential of membranes remains something of a mystery
cloaked in an uncomfortable equation and carries with it a
sense of uneasiness. This problem appears to be widespread.
Silverthorn (19) conducted a study of upper division undergraduates who had completed a semester of neurophysiology
that covered the Nernst and Goldman equations. She concluded that most students had only a superficial understanding of the ionic basis for the membrane potential (Vm). For
instance, the vast majority either couldn’t predict or couldn’t
explain the effect on Vm of changing extracellular K⫹.
In teaching Vm to second-year medical students, I have
found an approach that I believe takes the mystery out of this
concept. Additionally, it has proven successful in communi-
Illuminations
544
UNDERSTANDING THE RESTING MEMBRANE POTENTIAL
Vm ⫽ RT ⁄ FZ · ln共Kin ⁄ Kout兲.
Table 1. Assumptions
Assumption
1. Ions move randomly and independently.
2. Through random motion, ions diffuse down their concentration gradient.
3. Charged ions are attracted by the opposite and are repelled by the same
charge.
4. Charges can interact across a physical barrier.
5. V ⫽ IR
We ⫽ Wd ,
VmFZ ⫽ RT · ln共Kin ⁄ Kout兲 ,
which when rearranged, gives us the Nernst equation:
Fig. 1. Ions are in motion. A: flux of ions
observed as they diffuse through a frame
from a source of high concentration. B: neuron concentration gradient as established by
Na⫹/K⫹ ATPase. K⫹ is 140 mM inside the
cell and 4 mM outside the cell.
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A second energy source, which is electrical energy, is
established as a consequence of diffusion across the membrane. In the ground state, positive and negative ions on both
sides of the membrane balance one another exactly. This
balance is disrupted by placing an ion channel in the membrane
that is selective for K⫹ ions and impermeable to other ions,
including Na⫹ and negatively charged ions. Every time a K⫹
ion exits through the channel, a negative partner has been left
behind (Fig. 3, A and B). This results in an accumulation of
negatively charged ions on the inside of the membrane and
positively charged ions on the outside of the membrane (Fig.
3C). The oppositely charged ions attract each other across the
membrane. Individual ions still move randomly, but now a bias
or drift is imposed upon the random motion due to electrical
attraction. The alignment of positive and negative charge
across the membrane establishes an electric potential across the
cell membrane. The work done is described by the equation
We/mole ⫽ VmFZ. This simply states that amount of work that
can be done equals the strength of the membrane potential (Vm)
times a constant known as Faraday’s number (F) times the
number of elementary charges per ion (Z). The positive and
negative ions are closely apposed across the membrane, and
consequently overall charge neutrality is preserved.
As more K⫹ ions leave the cell, the potential increases,
which results in an ever greater bias on the motion of the
positive ions outside the cell, resulting in a greater number of
K⫹ ions colliding with the membrane’s outer surface. This will
increase the number of K⫹ ions entering the channel from the
outside. Equilibrium is achieved when Vm grows sufficiently
strong such that the number of K⫹ ions entering the channel
from the outside due to electrical drift is equal to the number
entering from the inside due to diffusional collisions. At this
point, the diffusional and electrical forces balance and we have
This is how Vm is established. Its source is the alignment of
positive and negative ions on either side of the membrane. This
creates an electric field across the membrane, which biases the
movement of ions in relationship to the membrane and orients
transmembrane proteins by acting upon their charged residues.
Changes in Vm result in changing the orientation (conformation) of membrane proteins, thereby effecting a rapid signal
(Fig. 3D). It is important to note that with the exception of
those charges lined up along the membrane surface, all charged
ions inside and outside the membrane still have a partner of the
opposite sign, preserving net neutrality. The unaccompanied
charges aligned along the membrane interact with their opposites on the other side, preserving charge neutrality. It requires
only a miniscule number of K⫹ exiting to establish Vm, and
consequently this ion movement has no meaningful effect on
ion concentrations inside or outside the cell.
It is clear that the key to establishing Vm is having an ion
channel that is selective for K⫹ ions. A channel that permitted
both positive and negative charges to pass through it would
never lead to a membrane potential, because each time a K⫹
ion exited the cell, it would attract a negative partner, thereby
maintaining charge neutrality. Similarly, if the channel was
equally permeable to Na⫹ ions, then they would be able to flow
down their concentration gradient, bringing positive charge
into the cell. To understand K⫹ channel selectivity, we need to
consider the manner in which charged ions interact with water
molecules. Each positively charged ion coordinates the H2O
molecules such that it orients the negatively charged oxygen
atom toward it (Fig. 4A). Each species of ion has a certain
number of H2O surrounding it (e.g., 8 for K⫹), and very
importantly, each ion has a characteristic distance at which it
interacts with the oxygen. For a K⫹ ion, this distance is 2.7 Å,
whereas it is 2.3 Å for a Na⫹ ion. Energetically, it is highly
unfavorable for a K⫹ ion to interact with the oxygen at the
characteristic distance of a Na⫹ ion and vice versa. This is the
key to selectivity for ion channels. A channel selective for K⫹
ions mimics the aqueous environment for these ions by presenting oxygen atoms in its amino acid residues in such a
manner that a K⫹ ion can interact with them at precisely 2.7 Å,
a distance highly favorable for K⫹ ions and highly unfavorable
for other ion species (Fig. 4A). In 2003, Jiang et al. (8)
demonstrated that the K⫹ channel possesses precisely this
property. It spans the membrane and has a pore that will
allow only for K⫹ ions to pass through due to the arrangement of its residues (Fig. 4C). The manner in which the
Illuminations
UNDERSTANDING THE RESTING MEMBRANE POTENTIAL
545
channel pore mimics the aqueous environment is demonstrated in Fig. 4D.
To recapitulate, the key to creating Vm is the establishment
of a concentration gradient for a charged ionic species across
the cell membrane together with the presence of an ion channel
that is selective for that particular ion. This results in the ion
exiting the cell through its channel, thereby creating a charge
imbalance. As the charge imbalance increases, the resulting
electric field imposes a drift upon the ions that is opposite to
the direction of diffusion. Equilibrium is established when
the electrical potential grows sufficiently strong such that it
just balances the diffusional force. At that point, there are
equal numbers of ions entering the channel from the outside
due to electrical drift as there are exiting due to diffusional
force.
Once this concept is mastered, it is easy for the student to
understand the behavior of Na⫹ and other ions, given their
concentration gradients. Figure 5 lists the extracellular and
intracellular concentrations for the membrane-permeable ions,
their ratios, equilibrium potentials, and their typical effect on
Vm. In company with the ionic ratios, the triangles represent
the direction and steepness of the ionic gradients (albeit not to
scale). In addition to the actions of K⫹ and Na⫹ that have
already been discussed, Clⴚ ions flowing down their concentration gradient bring negative charge into the cell, resulting in
membrane hyperpolarization. The action of Ca2⫹ ions is more
Fig. 3. Establishment of electric field. A: K⫹
ions leave the cell through selective channels, leaving behind a negative ion (dashed
circle). B: unaccompanied, oppositely charged
ions will attract each other across the membrane (dashed oval). C: unaccompanied ions
orient themselves such that they interact
across the membrane. D: the resulting electric field orients the charged residues contained in membrane proteins.
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Fig. 2. K⫹ gradient. A: higher concentration of K⫹ inside the cell leads to a greater no. of collisions on the inside surface. B: K⫹ will tend to flow out of a K⫹
channel in membrane. C: K⫹ as energy source; collision bias will turn wheel in 1 direction.
Illuminations
546
UNDERSTANDING THE RESTING MEMBRANE POTENTIAL
subtle. The main effect of Ca2⫹ ions entering the cell is to
activate Ca2⫹-dependent K⫹ channels. This results in a large
egress of K⫹ that hyperpolarizes the membrane. So despite the
fact that positive Ca2⫹ ions enter the cell, their effect is
swamped by the exit of a much greater number of K⫹ ions. The
manner in which multiple conductances result in Vm is discussed in an earlier paper (2).
A further point that may be of interest to more advanced
students concerns the direct contribution of the Na⫹/K⫹ ATPase
to Vm. As discussed above, the Na⫹/K⫹ membrane pump mainIon
K+
Na+
Fig. 5. Ion gradients and equilibrium potentials determined for skeletal muscle based on
Hille (7). ␺Triangles represent the relative
ionic gradients (not to scale); *main effect of
Ca2⫹ entering the cell is to activate Ca2⫹dependent K⫹ channels, resulting in a large
outward K⫹ current that hyperpolarizes the
cell.
Extracellular
(mM)
4
145
tains ionic concentrations by exchanging 3 Na⫹ (out) for 2 K⫹
(in) with each cycle. The net egress of one positive charge with
each cycle represents a negative current entering the cell. Recalling that V ⫽ IR (Table 1), we see that a negative current flowing
across the membrane will contribute to Vm by causing it to be
more negative. This has been demonstrated to be true in many
cells, and the portion of Vm that is provided by the pump varies
with cell type, depending upon things such as size, membrane
resistance, current size, etc. For instance, in a molluscan neuron, the
activity of the Na⫹/K⫹ ATPase contributes ⫺10 mV to Vm (5, 6).
Intracellular
(mM)
155
10
Ratio
Out/in
.03
12
ψ
Equilibrium
Potential
-98
Typical effect on Vm
Hyperpolarizing
+67
Depolarizing
Cl-
120
4
30
-90
Hyperpolarizing
Ca2+
1.5
.0001
15,000
+130
*Hyperpolarizing
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Fig. 4. Potassium selective channel mimics
the aqueous environment. A: K⫹ ion in water. B: K⫹ channel presents O2 molecules at
the optimal distance, imitating aqueous environment. C: crystal structure of K⫹ channel. D: K⫹ ions in water and in K⫹ channel.
Illuminations
UNDERSTANDING THE RESTING MEMBRANE POTENTIAL
547
DISCUSSION
AUTHOR CONTRIBUTIONS
The approach described in this paper provides an intuitive
understanding of how Vm is established by the concentration
gradient for K⫹ ions. This approach is complimentary to other
approaches, including a variety of demonstrations, laboratory
exercises, and computer simulations. For example, Wright’s
(21) refresher on the generation of the resting potential provides a careful and thorough analysis of the Nernst equation,
provides an excellent explanation of how the equation is
developed, and leads to a deep understanding of the process at
the level of the actual number of ions involved. One can find a
variety of either computer- or web-based simulations and
exercises that teach Vm, including those reported by Barry (1)
and by Dwyer et al. (3). There are also multiple simulations
and laboratory demonstrations of Vm. Milanick (11) has developed a simple and elegant visualization of ionic gradients
contributing to membrane potential through color changes in a
solution. This approach uses different colored solutes to represent each ionic species, color intensity as an indicator of
concentration, and valves to represent ionic conductances.
Procopio (15a) uses hydraulic analogs to teach the Vm concept.
Using valves to connect ionic gradient reservoirs to the Vm
reservoir, this author represents different equilibrium potentials
by the height of the various water columns in each reservoir
and models cell capacitance by the size of the Vm reservoir.
The height of the water column in the Vm reservoir represents
the membrane potential and can be directly related to the
heights of the columns in the ionic gradient reservoirs and the
relative degree of opening of their valves (11). Moran et al.
(12) developed a simple and inexpensive laboratory demonstration of the establishment of Vm by placing differing concentrations of K⫹H2PO4⫺ on opposite sides of a dialysis
membrane and using a pH meter as the detector. A similar
approach was taken by Shlyonsky (18) in which polycarbonate
filters were used to establish bioelectric potentials that could be
recorded using a pH meter.
There have been several living preparations used to demonstrate bioelectrical potentials. Thurman (20) developed a preparation using frog Sartorius muscle for demonstrating the role
of K⫹ in setting Vm and also used the exercise to teach students
hypothesis testing. Ribiero-Filho et al. (16) used the contractions in a ring-like preparation from rat mesenteric artery as an
indicator of changes in membrane potential in response to
changes in ionic gradients. Schwab et al. (17) developed a
demonstration of Vm by measuring the membrane potential of
Xeonopus laevis oocytes in response to stepwise changes in
external K⫹. All of these approaches are synergistic with the
intuitive program described in this paper, and I believe that if
students first work through an intuitive understanding, these
complimentary experiences will be enhanced. A series of
PowerPoint slides that presents this approach is available from
the author on request.
D.L.C. conception and design of research; D.L.C. prepared figures; D.L.C.
drafted manuscript; D.L.C. edited and revised manuscript; D.L.C. approved
final version of manuscript.
No conflicts of interest, financial or otherwise, are declared by the author.
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REFERENCES