Biomedical Engineering Reference
In-Depth Information
E Field
K Drift
K Diff
Cl Drift
Cl Diff
333 mM [ KCl ]
Channel
167 mM [ KCl ]
500 mM [ RCl ]
Inside
Outside
+
18 mV
12.4.4 Goldman Equation
The squid giant axon resting potential is
60
mV
, which does not equal the Nernst
Na þ or
K þ . As a general rule, when
potential for
V m is affected by two or more ions,
each ion influences
V m , as determined by its concentration and membrane permeability.
The Goldman equation quantitatively describes the relationship between
and permeable
ions, but only applies when the membrane potential or electric field is constant. This situation
is a reasonable approximation for a resting membrane potential.
In this section, the Goldman equation is first derived for
V m
K þ and
Cl , and then extended
Na þ . The Goldman equation is used by physiologists to calculate the
membrane potential for a variety of cells and, in fact, was used by Hodgkin, Huxley, and
Katz in studying the squid giant axon.
Consider the cell membrane shown in Figure 12.9. To determine
K þ ,
Cl , and
to include
Cl ,
flow equations for each ion are derived separately under the condition of a constant electric
K þ and
V m
for both
Cl
K +
Outside
dx
Inside
Cl
K +
FIGURE 12.9 A cell membrane that is permeable to both K þ and Cl . The width of the membrane is dx ¼ d.
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