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CASE 3
A 6-year-old boy is brought to the family physician after his parents noticed
that he had difficulty moving his arms and legs after a soccer game. About
10 minutes after leaving the field, the boy became so weak that he could not
stand for about 30 minutes. Questioning revealed that he had complained of
weakness after eating bananas, had frequent muscle spasms, and occasionally
had myotonia, which was expressed as difficulty in releasing his grip or difficulty opening his eyes after squinting into the sun. After a thorough physical
examination, the boy was diagnosed with hyperkalemic periodic paralysis.
The family was advised to feed the boy carbohydrate-rich, low-potassium
foods, give him glucose-containing drinks during attacks, and have him avoid
strenuous exercise and fasting.
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What is the effect of hyperkalemia on cell membrane potential?
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What is responsible for the repolarizing phase of an action potential?
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What is the effect of prolonged depolarization on the skeletal
muscle Na+ channel?
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CASE FILES: PHYSIOLOGY
ANSWERS TO CASE 3: ACTION POTENTIAL
Summary: A 6-year-old boy who experiences profound weakness after exercise is diagnosed with hyperkalemic periodic paralysis.
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◆
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Effect of hyperkalemia on membrane potential: Depolarization.
Repolarization mechanisms: Activation of voltage-gated K+
conductance and inactivation of Na+ conductance.
Effect of prolonged depolarization: Inactivation of Na+ channels.
CLINICAL CORRELATION
Hyperkalemic periodic paralysis (HyperPP) is a dominant inherited trait
caused by a mutation in the α subunit of the skeletal muscle Na+ channel. It
occurs in approximately 1 in 100,000 people and is more common and more
severe in males. The onset of HyperPP generally occurs in the first or second
decade of life. HyperPP is neither painful nor life-threatening but can be disruptive to normal activities. Symptoms are muscle weakness and paralysis,
sometimes preceded by myotonia, fasciculations, or spasms. Fortunately, significant paralysis almost never occurs in intercostals or diaphragm muscles,
and so breathing is not impaired. Attacks can occur spontaneously but often
are triggered by exercise, stress, fasting, or the ingestion of large quantities of
K+ (eg, in bananas). For unknown reasons, exercise-induced paralysis always
follows exercise—it does not occur during exercise. Because exercise can produce hyperkalemia and hyperkalemia triggers HyperPP attacks, there must be
an additional mechanism that protects skeletal muscle during but not after
intense activity. The mechanisms that underlie the effects of HyperPP result
from several known mutations in the α subunit of the skeletal muscle Na+
channel that prevent it from closing effectively. Ineffective closing results in a
small, persistent inward current that continuously depolarizes the muscle
membrane; this lowers the action potential threshold, producing the hyperexcitability that results in fasciculations (spontaneous twitches) and spasms
under resting conditions. If the depolarization increases further, as occurs
when extracellular [K+] is elevated, the Na+ channels inactivate and remain
inactivated until repolarization occurs. This inactivation blocks action potential initiation in the muscle and produces paralysis. When extracellular [K+]
decreases, the depolarization is reduced, inactivation is removed, and the
paralysis is relieved. Amelioration of HyperPP attacks is attempted by reducing plasma K+ levels. Insulin promotes the transport of extracellular K+ into
intracellular compartments by activating the Na-K pump. Eating highcarbohydrate diets or pure glucose increases insulin secretion and thus
decreases extracellular [K+]. Conversely, fasting decreases insulin secretion
and can elevate extracellular [K+], increasing the chances of myotonia and
paralysis in HyperPP patients.
CLINICAL CASES
33
APPROACH TO ACTION POTENTIAL PHYSIOLOGY
Objectives
1.
2.
Know the mechanisms of the resting potential.
Understand the mechanisms of the action potential in axons and skeletal muscle.
Definitions
Action potential: A rapid, depolarizing change in membrane potential
(often overshooting, so that the potential transiently reverses) that is
used by excitable cells to convey all-or-none electrical signals quickly
from one point on the cell to the remainder of the cell.
Electrotonic conduction: The passive, exponentially falling, spread of a
difference in membrane potential between different membrane regions,
which occurs with potentials subthreshold for an action potential or with
perturbations of membrane potential in inexcitable membrane regions.
Nernst equilibrium potential: The membrane potential at which, for a
given ion, there is no net flow of the ion across the membrane, which
corresponds to the electrical force that exactly offsets the driving force
of the concentration gradient acting on that ion.
Resting potential: The electrical potential difference across the plasma
membrane in the absence of action potentials or synaptic potentials.
Voltage-gated channel: Pore-forming protein complexes that allow ions to
flow across a membrane, and which can be opened (or, in some cases,
closed) by a change in membrane potential.
DISCUSSION
The mechanisms that underlie the action potential cannot be understood without an understanding of how a resting membrane potential is generated. The
resting potential in nearly all mammalian cells is produced primarily by diffusion of K+ down its concentration gradient from inside to outside the
cell, whereas the membrane remains relatively impermeable to other ions. The
intracellular concentration of K+ is very high compared with the outside
concentration because K+ is pumped into the cell by the Na+-K+-ATPase
(adenosine triphosphatase) (see Figure 3-1). Because the membrane is effectively impermeable to intracellular anions, as K+ flows down its concentration gradient, it leaves behind anions. A transmembrane potential (Vm)
develops as the K+ efflux brings a positive charge to the region just outside the
membrane, leaving an equal amount of negative charge just inside the membrane. This process is self-limiting because as soon as a membrane becomes
permeable to K+ and K+ efflux begins, the resulting separation of the charge
generates an electrical driving force on the ions, and the electrical driving
34
CASE FILES: PHYSIOLOGY
2K+
β
Outside
α
3Na+
Inside
Figure 3-1. Na+-K+-ATPase pump. The α subunit is the catalytic subunit,
which uses adenosine triphosphate (ATP) for energy to drive the extrusion of
three Na+ ions for every two K+ ions taken into the cell. The β subunit is important for assembly and membrane targeting of the Na+-K+-ATPase. Pump activity can be blocked by cardiac glycosides, such as ouabain. (From Horisberger
JD, Lemas V, Kraehenbuhl JP, Rossier BC. Structure–function relationship of
Na-K-ATPase. Ann Rev Physiol. 1991;53:565. Reproduced, with permission,
from the Annual Review of Physiology, vol. 53. Copyright © 1991 by Annual
Reviews Inc.)
force soon equals the opposing chemical driving force (the K+ concentration
gradient). For K+ or any ion X, this equilibrium occurs at a Vm called the
Nernst equilibrium potential, which is defined as the electrical driving force
(EX) that exactly offsets the chemical driving force. The electrical driving
force is represented by the left side and the chemical driving force is represented by the right side of the Nernst equation:
EX =
RT [ X]o
In
[ X]i
zF
R is the gas constant, T is the temperature in degrees Kelvin, z is the valence
of the ion, F is the Faraday constant, and [X]o and [X]i are the ion’s extracellular and intracellular concentrations. In the case of K+ at 37°C and converting
to log10, the equation becomes
E k = 60 log
[K + ]o
[K + ]i
It is important to note that a given ion X is at equilibrium across the membrane
only when Vm = EX. Because of the relatively high intracellular concentrations
35
CLINICAL CASES
of K+ in mammalian cells, EK is always quite negative (eg, ∼ −90 mV).
Because of the pumping action of the Na+-K+-ATPase, the concentration gradient for Na+ is in the opposite direction (ie, [Na+]o >> [Na+]i), and thus ENa =
∼ +55 mV. However, in cells, such as glia, in which there is no significant permeability to Na+, Na+ influx makes almost no contribution to Vm.
In most cells, including all excitable cells, Vm ≠ EK, although the values are
often close. This is the case because the membrane is also permeable to other
ions, and it is the net effect of all ion permeability across the membrane that
determines Vm. In many axons, Vm is determined almost entirely by opposing
fluxes (or, in electrical terms, currents) carried by K+ and Na+. These can be
described, in terms of the ratio of permeabilities (α = PNa/PK) and ionic concentrations, by the Goldman-Hodgkin-Katz equation, which is closely
related to the Nernst equation:
Vm = 60 log
[K + ]o + α[ Na + ]o
[K + ]i + α[ Na + ]o
In an axon at rest, α = approximately 0.01, and so the contributions of the Na+
concentrations in the expression are slight, and Vm is close to EK (∼ −90 mV). In
many neuronal cell bodies or dendrites, PNa is somewhat greater than this when
the cell is at rest and Vm is more depolarized (eg, ∼ −65 mV). Permeabilities (P)
often are referred to by their electrical equivalents, conductances (g). Note that
an increase in extracellular K+, that is, hyperkalemia, will depolarize cells,
whereas hypokalemia will hyperpolarize cells.
An all-or-none action potential is generated in an axon when membrane
depolarization reaches a level at which voltage-gated Na+ channels open,
increasing PNa. This results in an inward current of Na+, which causes further
depolarization, which then opens additional Na+ channels. This regenerative
(positive feedback) cycle quickly produces an overshooting action potential.
In terms of the Goldman-Hodgkin-Katz equation, α quickly goes from
approximately 0.01 to 100, Vm becomes dominated by the Na+ concentration
gradient, and thus Vm approaches ENa at the peak of the action potential.
Axonal action potentials last only a few milliseconds because two mechanisms rapidly repolarize the membrane. One is the activation of voltagegated K+ channels that open with a slight delay compared with the Na+
channels, resulting in the delayed rectifier outward current carried by K+ ions.
Although this reduces α by increasing PK, a second depolarization-triggered
mechanism, Na+ channel inactivation, reduces α by decreasing PNa. Thus,
depolarization initially opens Na+ channels (activation) but then closes Na+
channels (inactivation), and the channels remain closed until the membrane
repolarizes to a level close to the normal resting potential. This means that
prolonged depolarization produced for example, by hyperkalemia, can make
excitable cells inexcitable.
The changes in permeability, expressed in terms of conductance (g), that
underlie the action potential in axons are shown in Figure 3-2. The mechanisms
36
CASE FILES: PHYSIOLOGY
E
Na+
Voltage or conductance
Membrane potential
+
Na
+
K
E K+
1 ms
Figure 3-2. The nerve action potential. The time course of changes in the Na+
and K+ conductance is depicted.
for repolarizing the membrane after each action potential (which is critical for
preventing summation of action potentials and permitting firing at high frequencies) are also responsible for the biphasic refractory period that follows
each action potential. Inactivation of Na+ channels completely prevents action
potential initiation, causing the absolute refractory period. After Na+ inactivation is removed by repolarization, the membrane remains less excitable than
normal during the relative refractory period, during which the delayed rectifier K+ channels are transiently open.
The action potential propagates because the depolarization and overshoot
in an active region (where voltage-gated Na+ channels are open) spread passively by electrotonic conduction to adjacent regions, depolarizing those
regions and triggering the same regenerative sequence when the neighboring
Na+ channels are opened by the electrotonically conducted depolarization.
Electrotonic conduction occurs because the positive Na+ ions entering the cell
in the active region are attracted to the net negative charge inside neighboring
membrane that is hyperpolarized, and neighboring anions are attracted to the
CLINICAL CASES
37
positive region inside the active membrane. The opposite current flow occurs
outside the membrane. These intracellular and extracellular currents combine
in a local circuit that quickly depolarizes membrane adjacent to an active
region.
Current density underlying electrotonic propagation of depolarization
(or hyperpolarization) declines exponentially with distance. The effectiveness of electrotonic propagation often is compared by using the space or length
constant λ, which varies with the square root of the diameter of the axon. This
means that electrotonic propagation of current in front of an active region projects farther in axons with larger diameters and therefore that conduction of
action potentials is faster in larger axons. The velocity of action potential
conduction also depends on how much time it takes for a region of membrane
to depolarize. This is characterized by the time constant τ, which varies
directly with membrane resistance Rm and membrane capacitance Cm. If Rm or
Cm is large, the rate with which a region of membrane can depolarize (or
hyperpolarize) is slow, and this reduces the velocity of action potential conduction. Mammals have increased action potential velocity by myelinating
many axons, which in effect reduces Cm. The most rapidly conducting axons
are both myelinated and have large diameters (ie, have small τ and large λ).
Demyelinating diseases such as multiple sclerosis profoundly decrease conduction velocity and cause serious neurologic problems.
COMPREHENSION QUESTIONS
[3.1]
The resting transmembrane potential (Vm ) of a nerve axon is essential
for signal generation. Instantaneous elimination of which of the following would most rapidly bring Vm close to 0 mV?
A. Active transport of K+ out of the cell
B. Active transport of Na+ out of the cell
C. Concentration gradient for Na+
D. High membrane permeability to K+
E. High membrane permeability to Na+
[3.2]
Hyperkalemia reduces the excitability of neurons and muscle cells.
Which of the following best describes the effect of increased extracellular potassium [K+]o?
A. Depolarizes the cell, thus reducing action potential amplitude
B. Depolarizes the cell, thus inactivating voltage-gated Na+ channels
C. Hyperpolarizes the cell, which increases the action potential
threshold
D. Increases the activity of the Na-K-ATPase, which hyperpolarizes
the cell
E. Stimulates endocytosis of Na+ channels
38
[3.3]
CASE FILES: PHYSIOLOGY
The velocity of action potential conduction is noted to be affected by
various parameters. If the conduction velocity were found to be augmented, which of the following characteristics would most likely be
decreased?
A.
B.
C.
D.
E.
Action potential amplitude
Effective membrane capacitance
The concentration gradient for Na+
The rate at which Na+ channels open in response to depolarization
Na+ channel density uniformly along a fiber
Answers
[3.1]
D. The immediate cause of the resting potential is the high membrane permeability to K+ compared with other ions; if this permeability were to be eliminated, Vm would instantly depolarize to
within several mV of 0 mV. It would not quite reach 0 mV because
of the electrogenic effect of the Na+-K+-ATPase (which pumps three
Na+ ions out for every two K+ ions pumped in). The diffusion of K+
down its concentration gradient in the absence of diffusion of anions
out of the cell or diffusion of other cations into the cell causes a
slight separation of charge across the membrane that generates most
of the resting potential. The active transport of K+ into the cell (not,
as in answer A, out of the cell) is necessary for setting up the concentration gradient that results in the diffusion of K+ out of the cell.
This gradient (and therefore Vm) would take a long time to dissipate
if active transport were stopped. Because the membrane is effectively impermeable to Na+ at rest, the transport and concentration
gradient for Na+ has very little effect on the resting potential
(answers B, C, and E).
[3.2]
B. Sustained depolarization, as occurs with hyperkalemia, inactivates voltage-gated Na+ channels, which remain inactivated until the
membrane repolarizes, thus blocking action potential generation. If
action potentials are generated, their amplitude will be reduced
(answer A), but this is a consequence rather than a cause of reduced
excitability. Hyperpolarization also can reduce excitability by
increasing the depolarization needed to reach action potential
threshold (answers C and D), but this would be produced by
hypokalemia, not by hyperkalemia. There is no evidence that prolonged hyperkalemia decreases the number of Na+ channels in the
membrane (answer E).
[3.3]
B. Effective membrane capacitance is decreased in many mammalian
axons by myelination—the tight wrapping of many glial membranes
around the axon, which is functionally equivalent to increasing the
thickness of the membrane. Because conduction velocity is inversely
CLINICAL CASES
39
related to membrane capacitance, which is related inversely to effective
membrane thickness, a decrease in membrane capacitance increases
conduction velocity. Decreasing action potential amplitude (answer A)
will decrease rather than increase action potential velocity (see Case 8),
as will decreasing the concentration gradient for Na+ (because this will
reduce action potential amplitude). In addition, decreases in the opening rate or density of Na+ channels will decrease conduction velocity.
PHYSIOLOGY PEARLS
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The resting potential is generated by the high permeability of the
membrane to K+ compared with other ions, which allows a very
small amount of K+ to diffuse out of the cell in the absence of net
diffusion of other ions, causing a charge separation across the
membrane.
The resting potential and action potential in simple excitable systems, such as axons, that are permeable only to K+ and Na+, can
be described by the Goldman-Hodgkin-Katz equation, which
states that Vm is determined by opposing currents carried by K+
and Na+, which are determined entirely by (1) the ratio of permeabilities to K+ and Na+ and (2) their concentration gradients
across the cell membrane.
An action potential is generated when membrane depolarization
reaches a level at which voltage-gated Na+ channels open,
increasing PNa (or, in electrical terms, gNa), which results in an
inward current of Na+, which causes further depolarization, opening additional Na+ channels in a positive feedback cycle.
Inactivation of Na+ channels during an action potential prevents subsequent action potential initiation during the brief absolute
refractory period, whereas the relative refractory period continues shortly thereafter because the delayed rectifier K+ channels
remain open for a somewhat longer period.
The spread of depolarization in front of an active region of membrane during an action potential occurs by electrotonic propagation, which is characterized by an exponential decay of the
depolarization with distance along the fiber.
The velocity of action potential conduction is increased by myelinating axons, which decreases their effective membrane capacitance, and by increasing the fiber diameter, which decreases the
intracellular resistance.
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CASE FILES: PHYSIOLOGY
REFERENCES
Byrne JH. Resting potentials and action potentials in excitable cells. In: Johnson
LR, ed. Essential Medical Physiology. San Diego, CA: Elsevier Academic Press;
2003:71-96.
Moczydlowski EG. Electrical excitability and action potentials. In: Boron WF,
Boulpaep EL. Medical Physiology. Philadelphia, PA: Elsevier Science;
2003:172-203.