resting Em because Em reflects not only the
concentration gradients of individual ions
(i.e., the equilibrium potentials) but also
the relative permeability of the membrane to
those ions. If the membrane has a relatively
higher permeability to one ion over the oth-
ers, that ion will have a greater influence in
determining the membrane potential.
Membrane permeability for an ion deter-
mines the movement of an ion being driven by
a net electrochemical force. Because this ion
movement represents an electrical current, it
is common to speak in terms of ion conduct-
ance (g), which is defined as the ion current
divided by the net voltage (net electrochemical
force) acting on the ion. Membrane permeabil-
ity and ion conductance are related in that an
increase in membrane permeability for an ion
results in an increase in electrical conductance
for that ion. Putting these concepts together, it
is possible to derive an expression that relates
membrane potential (Em) to the relative con-
ductances of all ions and their equilibrium
potentials as shown in the following equation:
Em = g'K*(EK) + g'Na+(ENa)
+ g'Ca++(ECa)
In Equation 2-3, the Em is the sum of the indi-
vidual equilibrium potentials for K+, Na+, and
Ca++, with each multiplied by the membrane
conductance for that particular ion relative to
the sum of all ion conductances. For exam-
ple, the relative conductance for K+ (g'K+) =
gK+/(gK+ + gNa+ + gCa++). If the equilibrium
potentials for K+, Na+, and Ca++ are calculated
using the concentrations shown in Figure 2.1,
then Equation 2-3 can be depicted as follows:
Em = g'K+(-9 6 mV)
Eq. 2-4
+ g'Na+ ( + 52 mV)
+ g'Ca++(+134 mV)
In a cardiac cell, the individual ion concentra-
tion gradients change very little, even when Na+
enters and K+ leaves the cell during depolariza-
tion. Therefore,
changes in Em primarily result
from changes in ionic conductances.
The rest-
ing membrane potential (-90 mV) is near the
equilibrium potential for K+ (-96 mV) because
g'K+ is high in the resting cell, while g'Na+ and
g'Ca^ are low. Therefore, the low relative con-
ductances of Na+ and Ca” multiplied by their
equilibrium potential values causes those ions
to contribute little to the resting membrane
potential. When g'Na+ increases and g'K+
decreases (as occurs during an action poten-
tial), the membrane potential becomes more
positive (depolarized) because the sodium
equilibrium potential has more influence on
the overall membrane potential. Similarly, a
large increase in g'Ca+, particularly when g'K+
is low, will also result in depolarization.
In Equation 2-3, ion concentrations (which
determine the equilibrium potential) and ion
conductances are separate variables. In reality,
the conductance of some ion channels is influ-
enced by the concentration of the ion (e.g.,
K+-sensitive K+ channels) or by changes in
membrane potential (e.g., voltage-dependent
Na+, K+, and Ca^ ion channels). For exam-
ple, a decrease in external K+ concentration
(e.g., from 4 to 3 mM) can decrease gK+ in
some cardiac cells and lead to a small depo-
larization (less negative potential) instead of
the hyperpolarization (more negative poten-
tial) predicted by the Nernst relationship or
Equation 2-3. In some cells, small increases in
external K+ concentration (e.g., from a normal
concentration of 4 to 6 mM) can cause a small
hyperpolarization owing to activation of K+
channels and an increase in gK+.
High concentrations of potassium are
added to cardioplégie solutions used
to arrest the heart during surgery.
Using the Nernst equation, calculate an
estimate for the new resting membrane
potential (Em) when external potassium
concentration is increased from a
normal value of 4 to 40 mM. Assume
that the internal concentration remains
at 150 mM and that K+ and other ion
conductances are not altered.
Maintenance of Ionic Gradients
Membrane potential depends on the main-
of ionic
across the membrane. The maintenance of
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