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CHAPTER 2
THE RESTING POTENTIAL
In the last chapter, the idea that the nervous system is a huge electrical system designed for
communication was introduced. Neurons act by conducting electrical pulses called action
potentials along their axons, and one neuron communicates with another neuron by releasing
chemical neurotransmitters when an action potential invades the axon’s terminal. The effect of
the release of neurotransmitter is that the chemical binds to receptors on the postsynaptic neuron
and opens pores in its receptors. The opening of pores then allows positive charges to enter the
cell, and if the interior of the postsynaptic cell becomes sufficiently positive, an action potential
is generated at the axon hillock of the postsynaptic cell. The action potential then propagates
down the axon and the whole cycle is repeated.
But exactly what an action potential is and how it is created was not described. Indeed, all
of the electrical features and electrical terms, which are fundamental for the operation of
neurons, were used in very vague ways and were not explained. In this chapter, the electrical
nature of cells will be explained in greater detail. Subsequent chapters will explain how the
electrical features described here are used to evoke highly specialized electrical signals, action
potentials , which are unique to nerve and muscle cells.
Cells act as a battery because their membranes separate positive and negative charges
One feature of all living cells is that they act as a battery. This is true not only of nerve and
muscle, but all living cells. A battery is simply a device that separates positive and negative
charges. In cells, the separation is achieved such that the inside of the cell has a slightly larger
number of negatively charged molecules than the outside of the cell. The separation of charges
is due to two major things.
The First is that there is an imbalance of various ions on the inside compared to the outside
of the cell. These include sodium (Na
), potassium (K
), chloride (Cl
)
,
and calcium (Ca
++
) ions.
The concentration of these ions is different in the cytoplasm than it is in the extracellular fluids
in which the cells are bathed. Of particular importance is that the cytoplasm, or inside of the cell,
has a higher concentration of K
(indicated by [K
] i
) than does the extracellular fluid that bathes
the outside of the cell (indicated by [K
] o
). Conversely, the inside of the cell has a lower
concentration of Na
(indicated by [Na
] i
) than does the extracellular fluid (indicated by [Na
] o
The Second is that the cell membrane is semipermeable. Semipermeable simply means that
the membrane has pores or channels that allow only certain molecules to pass while preventing
others from crossing from one side to the other. The semipermeable membranes of all cells
allow K
ions to pass through easily, but act as barriers for the passage of Na
, Cl
, and Ca
++
ions.
Thus, K+ can readily go from the inside to the outside or in the opposite direction through the
channels, while Na+ is largely (but not completely) prevented from passing through those
channels.
How charges are separated across the membrane and a battery is produced
Next, let us consider how ion concentration differences and membranes with selectivities for
the passage of certain ions can lead to the development of a separation of charges and hence to
an electrical potential difference or voltage. For this purpose it is helpful to first consider a
simple set of conditions, as shown in Figure 1. We will then take the principles developed in the
simple situation and apply them to the more complex conditions in real cells.
Figure 1 shows a container that is divided into two compartments by a semi-permeable
membrane. A membrane's permeability to an ion species is a measure of how easily that ion can
pass through the membrane and thus go from one side of the compartment to the other side. The
membrane in the container in Fig. 1 has a high permeability to potassium (K
) ions but is
completely impermeable to all other ions. We now fill the container with water and the semi-
permeable membrane separates the container into two compartments. Next we put a small
amount of KCl (potassium chloride) into the right compartment and a larger amount of KCl into
the left compartment. In water, KCl ionizes into K
and Cl
ions, and since we put more KCl in
the left compartment and a smaller amount in the right compartment, the concentrations of both
K
and Cl
ions are higher in the left compartment than in the right compartment. Notice that in
this initial condition there are an equal number of K+ and Cl- ions on the left side (6 K+ and 6
Cl- in Fig. 1) and an equal number of K+ and Cl- ions on the right side (3 K- and 3 Cl-). Thus,
there is no net electrical imbalance in the left or right compartments because adding the positive
and negative charges in each compartment sums to zero. The key feature is that this electrical
neutrality in each compartment will change as ions diffuse across the membrane as described
below.
Fig. 1. A contained filled with water and
separated into two sections by a semi-
permeable membrane. The membrane is
permeable only to K+ and impermeable
to Cl-. Six molecules of KCl are placed
in the compartment on the left and 3
molecules of KCl are placed in the right
compartment. See text for further
explanation.
There are three key features about this system that are illustrated in Figs. 2 and 3. You
should keep the three features in mind since they will help you organize your thinking and
thereby help you understand how electrical potentials are established in cells.
- The first feature pertains to the laws of diffusion: specifically, that all molecules move
from a region of higher concentration to a region of lower concentration, and will continue to do
so until the concentrations become equal throughout. This aspect of diffusion is really an energy
that can be harnessed to do work. In the case of the container in Figs. 1-3, K+ diffuses from a
region of higher concentration, in the left compartment, to a region of lower concentration, in the
right compartment. This movement of K+ from the left to the right compartments is driven by
the concentration difference of K+ in the two compartments.
- The second feature is that when a molecule of K
leaves the left compartment, it carries
with it a positive charge and leaves behind an extra negatively charged Cl
molecule. The Cl
is
“extra” because it no longer is neutralized by a positively charged K
. Notice what is happening
electrical potential, that counterbalances the concentration force is called the equilibrium potential
for that ion. Since the container was permeable only to K+, the potential in this case is referred to
as the potassium equilibrium potential, abbreviated as E
K+.
Fig. 3. Diffusion of K+ continues until the concentration force driving K+ from the left into the right
compartment (black arrow) is exactly balanced by the electrical force driving K+ in the opposite direction
(red arrow), from the right into the left compartment. The value of this electrical force is called the
equilibrium potential for that ion. In this case, it is the equilibrium potential for K+, E k
.
The value of the equilibrium potential for an ion depends on the ion’s concentration
difference
Another feature should also be apparent: The greater the concentration difference between
the two compartments, the greater the electrical force (potential difference) has to be at
equilibrium to counter-act the concentration force. Stated differently, the greater the
concentration difference for the permeable ion, K
in this case, the more negative the left
compartment has to be to counteract the concentration force, i.e., the larger the equilibrium
potential for that ion has to be. This feature is illustrated in Fig. 4 by three containers, where
each container has two compartments with different concentrations of KCl. Figure 4 illustrates
that larger concentration differences require larger electrical differences to achieve an
equilibrium (for every ion driven into the right compartment by its concentration force, an equal
number of ions will be attracted back to the left compartment by the electrical force). But
exactly what value does the voltage difference have to be to counter a particular concentration
difference? That value is given by an equation from physical chemistry called the Nernst
Equation.
Fig. 4. Greater concentration differences of the permeable ion generate greater concentration forces
(black arrows) driving the ions from the left to the right compartments in the examples shown. The
greater concentration forces require greater electrical differences (red arrows) to balance the concentration
forces to achieve equilibrium. Here the original concentration differences are shown. The value of each
concentration force is indicated by the thickness of the black arrows and the value of the electrical force
required to counteract that concentration force is indicated by the thickness of the red arrows. Each
equilibrium potential is indicated by the size of the + and – signs beneath each container.
The Nernst Equation
The Nernst equation is a statement of the equilibrium condition for a single ion species
across a membrane that is permeable only to that ionic species. What the Nernst equation tells
you is what electrical force (electrical potential E in equation below) has to act on that ion in
order to exactly balance the concentration force acting on the same ion. The Nernst equation is:
E=
RT
zF
ln
[I]
o
[I]
i
where
E = the membrane potential in mV
R = the gas constant
T = absolute temperature
F = the Faraday (the charge in coulombs carried by a mole of monovalent ions)
z = the valence of the ion (including sign! The valence is +1 for K
and Na
and - 1 for Cl
)
ln = natural log, i.e. log to base e
[I]
o
= the concentration of a particular ion outside the cell
[I]
i
= the concentration of that same ion inside the cell
are permeable only to K
+,
, and K
+,
is 10 times more concentrated on the inside of the cell than on
the outside. The Nernst potential shows that the inside of the cell will have to be - 58 millivolts
(mV), more negative on the inside relative to the outside. That negativity, - 58 mV, will attract
back, into the cell, an equal number of positively charged K+ ions that are driven out of the cell
by the higher concentration of K+ on the inside. Similarly, the cell on the right has channels
permeable only to Na
, and the concentration of Na
in this cell is 10 times greater outside of the
cell than inside. The equilibrium potential for Na
is +58 millivolts, but here the inside of the
cell has to be 58 mV more positive than the outside in order to counter the concentration force
driving Na
ions into the cell.
In many respects the condition of the “cell” on the left resembles the situation occurring
across the cell membrane in real cells. The plasma membranes of cells are selectively permeable
to ions, similar to the membrane separating the two compartments of the left container we
considered above. Cell membranes are impermeable to large organic anions existing inside the
cell, such as aspartate, isothionate, and other amino acids as well as proteins and are even
impermeable to water. In addition, cell membranes are relatively impermeable to all ions except
potassium; hence, the membranes of cells are said to be "semi-permeable." The permeability of
the membrane is set by the permeabilities of the various ion channels that exist in the membrane.
We mentioned such channels earlier in this chapter and will discuss the variety of ion channels
that occur in cells in greater detail in later chapters.
All Cells have a Resting Potential Determined Largely by Potassium
A simple equation, the Nernst equation, allows you to determine what the equilibrium
potential would be for a particular ion if the membrane separating two solutions is permeable
only to that ion. The Nernst equation tells you what voltage (electrical force) is required to
counter-balance a particular concentration difference of a particular ion. The equation is E=58/z
log [ion] o
/[ion] i
, where z is the valance of the ion. In words, it simply says that the greater the
concentration difference, the larger the electrical force, E, necessary to counterbalance that
concentration difference.
The Nernst equation is accurate for containers with perfect semi-permeable membranes but
can the Nernst equation predict the electrical state of real neurons? As mentioned previously, all
cells, including neurons and muscle cells, have unequal concentrations of all ions on the cell
interior compared to the extracellular fluids. Moreover, all cells are very permeable to K+ and
relatively impermeable to Na+ and other ions. As we shall see below, the Nernst equation is
good at predicting the electrical state of neurons, but its predictions always have a slight error.
The error is because the membranes of real cells are not perfectly semi-permeable, but rather
have much greater permeability to K+ than other ions, but still are slightly permeable to Na+ and
Cl-. That slight permeability for Na+ in particular, is responsible for the slight difference
between the potential that the Nernst equation predicts and the potential that we actually record
in a cell. Let’s explore the reasons for this error below by considering a real cell.
The Nernst Equation does Not Provide a Perfect Prediction of a Neuron’s Resting Potential
As an example cell, let us consider the K+ concentration difference in the squid giant axon.
The squid, as we shall see in later chapters, has played a major role in our understanding of how
action potentials are generated. In that animal, the K+ concentration in the interstitial
(extracellular) fluid is 20 mM and the K+ concentration inside the cell is 400 mM. The Nernst
equation predicts that the equilibrium potential for K+ would be - 75.46 millivolts (mV). That is,
for this particular K+ concentration difference, the inside of the cell would be - 75.46 mV. When
the interior of the cells is at this potential, - 75.46 mV, the same number of K+ ions will be
attracted into the cell as would be expelled from the cell by that particular concentration
difference.
The actual resting potential of the squid giant axon can be accurately measured and is only
about - 70 mV. The resting potential is the electrical state of the cell (the voltage across its
membrane) when it is not active and thus not generating action potentials. The resting potential
of - 70 mV is not exactly equal to E k
, which is - 75.46 mV, but close to it.
The reason that the actual resting potential of the cell is not equal to E k
is that both Na+ and
Cl- play a small role in determining the electrical state of the cell (the cell's resting potential).
Remember, the membrane is not absolutely impermeable to Na+. Indeed, both the concentration
and electrical forces try to drive Na+ into the cell; the concentration force tries to drive Na+ in
because Na+ is much more concentrated in the extracellular fluid than in the cytoplasm, and the
electrical force attracts it into the cell because the cell interior has an excess of negative charges
(it is - 70 mV) that pulls the positively charged Na+ ions into the cell. If the cell membrane of a
squid were permeable only to Na+, the cell's resting potential would be equal to E Na
, which can
also be calculated from the Nernst equation ( the [Na]o is 450 mM and [Na]i is 50 mM). From
the Nernst equation, E Na
is +55 mv. That is, the inside of the cell would have be very positive,
+55 mv, to counterbalance the concentration force driving Na+ into the cell). Based on
concentrations of Cl-, the Nernst equation tells us that the equilibrium potential for Cl- is - 67 mv.
The Concentration Gradients of All Ions Should Run Down
A problem now arises since the resting potential is determined not only by K+ but also by
Na+ and Cl- (because the membrane is slightly permeable to those ions). To understand why the
permeabilities for Na+ and Cl- create a major problem, let us first consider the conditions that
would occur if the cell’s membrane were permeable only to K+ and not to any other ion. If that
were the case, then the resting potential would be equal to the K+ equilibrium potential, whose
exact value is given by the Nernst equation. What this also means is that there would be no net
movement of K+ ions into or out of the cell at equilibrium; for each K+ ion driven out of the cell
by the concentration force, one of K+ ion would be pulled back into the cell by the electrical
force. In other words, an equilibrium would be reached in which there is no net movement of
K
ions across the membrane. Under these conditions, the ion concentration gradients across the
membrane would persist indefinitely because no other ion could cross the membrane and the net
movement of K+ ions is zero at equilibrium. Indeed, that is exactly what the term “equilibrium
potential” means; for each K+ ion driven out of the cell by the concentration force, one of K+ ion
would be pulled back into the cell by the electrical force.
However, the membrane is not perfect; that is, it is not permeable only to K+, but to lesser
degrees is also permeable to Na
and Cl
. Because of these multiple permeabilities, the
concentration gradients of K+, Na+ and Cl- will run down, and disappear completely over time.
To show why concentration gradients will run down, let us consider Na+. Even if the
permeability of the membrane to Na
is small, the higher outside concentration tries to drive
Na+ into the cell and the negative cell interior tries to pull Na+ into the cell. Although the forces
driving Na+ into the cell are large, very little Na+ actually enters the cell because of the very low
permeability. However, and this is the key point, enough Na
will eventually enter the cell to
begin to cause a significant rise in its internal concentration. In addition, as Na
comes into the
cell it will, of course, neutralize some of the negative charges inside of the cell. When this
happens, the electrical potential will not be negative enough to hold K+ in the cell, and thus a
little more K+ will leave the cell tending to bring the membrane potential closer to the K+
equilibrium potential, and thus to a more negative value.
Thus, the Na-K pump itself is actually separating charges because it pumps more positive Na+
charges out of the cell than it pumps K+ into the cell. In such cases the operation of the pump is
said to be electrogenic. The Na-K pump, even in these cases where it is electrogenic, makes only
a very small (a few mV) contribution to the resting membrane potential. It is the operation of
these pumps in the cell membrane that maintains a steady-state distribution of ions across that
membrane. Although there is a net movement of Na+ and K+ ions across the membrane (Na
into the cell and K out of the cell), the net movements of those ions are counterbalanced by the
activity of the pump. In short, the pumps do not establish the resting potential, but rather their
purpose is to maintain the concentration gradients so that neurons can retain their resting
potentials even though they continuously lose K+ and continuously gain Na+.
For those of you who are interested in pharmacology, I should mention there is a drug
known as ouabain, which inhibits the activity of this Na-K pump. The action of ouabain is
similar to a more commonly known drug called digitalis. Digitalis is given in small doses to
victims of heart attack because it serves to increase the force of contraction of the heart. The
mechanism by which the contractile force in the heart is increased by digitalis will be considered
when we take up cardiac muscle.
The Resting Potential is given by Goldman-Hodgkin-Katz Equation
So how do all of the different values for the equilibrium potentials for Na+, K+ and Cl- fit
together to account for the actual resting potential of the cell? The answer is that they all
contribute, but their contribution is weighted by the relative permeability of each ion. Since K+
has the greatest permeability, it receives the greatest weight and thus makes the largest
contribution. Na+ is much less permeable and contributes only slightly to the resting potential.
Notice, however, that even a slight contribution by Na+ subtracts slightly from the much larger
contribution of K+. The reason is that the small influx of positive charges carried by Na+ just
slightly neutralizes the excess negative charges inside the cell.
The calculation of the resting potential can be made from the Goldman-Hodgkin-Katz
(GHK) equation, an equation similar to but slightly more complex than the Nernst equation. The
GHK equation takes the concentration gradient of each ion into account but weights the
contribution of each according to the ion's relative permeability. The equation is:
Erest = 58 log
P
Na
[Na]
o
P
Na
[Na]
i
P
K
[K]
o
P
K
[K]
i
P
Cl
[Cl]
i
P
Cl
[Cl]
o
Where P refers to the relative permeability of that particular ion. We assign the relative
permeability of potassium (P K
) a value of 1.0. P Na
is 0.01 (1/100 the permeability of K+) and P Cl
is 0.01. With these values for the relative permeability and concentration gradients of each ion,
the resting potential of a cell can be calculated from the GHK equation, as shown on the
following page for the squid giant axon. Also shown is the E K
calculated from the Nernst
equation, which is - 75.4 mV. The membrane potential computed from the GHK equation is -
70.18 mV and is in remarkably close agreement with the actual resting potential of - 70 mV
measured with microelectrodes.
You may have noticed that for both the computation of the Nernst equation and the GHK
equation, the ratios of the K+ and Na+ concentrations are computed as [ion] o
/ [ion] I
while
chloride concentrations are computed as [ion] i
/[ion] o
. These reason for this is because the
valance of chloride is negative and thus would have a - 1 value in the initial portion of the
equation (58/z) whereas the valances of both Na and K are positive. To correct for the negative
valence in the portion of the equation that takes the log value of the ratio, the ratio for chloride is
simply reversed, thereby allowing the log values of the concentration ratios of ions with positive
and negative valences to be computed.
Changes in the Membrane Potential can Change the Direction in which Ions are Driven
In the sections above, I introduced the concept of a resting potential. The resting potential is
the electrical state of the cell when it is not receiving inputs from other cells (when it is at rest).
The resting potential is determined by the concentration differences of all ions in the cell
weighted by their relative permeability. However, almost all influences on neurons, whether
they come from other neurons or even from external stimulation as occurs in some sensory
neurons, change the resting potential. For example, it was pointed out in the previous chapter
that when transmitter is released at the synapse, it opens pores in the receptors of the
postsynaptic cell and allows positive charges to enter the cell. The positive charges change the
membrane potential. An action potential is a large change in membrane potential, as will be
explained in the next chapter. The resting potential, therefore, is a special case of the cell's
membrane potential; it is the cell’s membrane potential at rest, when there are no disturbances or
other influences impinging upon the cell.
Thus the membrane potential, or voltage across the membrane of a neuron is often changing
due to the synaptic inputs from other neurons or other forms of stimulation. For reasons that will
become clear in subsequent lectures, it is most important for you to understand what happens to
the drives on Na+ and K+ when the neuron's membrane potential is changed to a value that is
the black arrows provide a rough indicate of the strength of the concentration and electrical forces. The
arrow indicates the direction in which the force acts. Since the concentrations of each ion are constant,
the direction and strength of the concentration force does not change with membrane potential; the
concentration force driving K+ is the same at all membrane potentials as is the concentration force
driving Na+. Only the electrical force changes with membrane potential. The red arrows indicate the net
strength and direction of the electrical and concentration forces for the different values of membrane
potential. The net strength is the difference between the concentration and electrical forces. A thin
double headed arrow indicates no net drive on the ion; that the two forces have equal strengths but act in
opposite directions.
A summary of the resting potential
Certainly the resting potential is one of the most difficult concepts in biology to understand.
Yet an understanding of the resting potential is absolutely vital to understanding of the nervous
system. Let me summarize the major points of this chapter.
- The resting potential exists because of concentration differences of Na
, K
, and Cl
across
the membrane.
- The major determinant of the resting potential is K
. K
ions maintain the resting membrane
potential by diffusing across the membrane (down their concentration gradient) and thus
separating charge across the membrane.
- Although K
is considered the primary ion underlying the resting membrane potential, the
actual resting potential will not equal E K
because a small amount of Na
continuously leaks
into the cell.
- The exact magnitude of the resting membrane potential thus depends on the weighted
contributions of the several ions moving across the membrane, expressed formally by the
Goldman-Hodgkin-Katz equation.
- The resting potential is a metabolically dependent phenomenon in that an energy-requiring
Na
- K
exchange pump is ultimately required to maintain (note maintain, not generate) it. If
the pump is blocked, say by an inhibitor of its activity, then the resting membrane potential will
run down and disappear. However, the resting potential will not disappear immediately, but
rather in a matter of hours, the time it takes for sufficient amounts of Na
to leak in and
sufficient amounts of K
to leak out and cause their concentration gradients to disappear.
