Biomedical Engineering Reference
In-Depth Information
Na
þ
and
K
þ
Subtracting both the capacitive and leakage current from
I
m
leaves only the
Na
þ
and
K
þ
currents, Hodgkin and Huxley substituted a large
currents. To separate the
Na
þ
in the external solution. This eliminated the
Na
þ
current
impermeable cation for
K
þ
current. Returning the
Na
þ
current to the external solution allowed
and left only the
Na
þ
current to be estimated by subtracting the capacitive, leakage, and
K
þ
currents
the
Na
þ
and
K
þ
currents due to a clamp voltage of
from
20 mV are shown in
Figure 12.25. Since the clamp voltage in Figure 12.25 is above threshold, the
I
m
.The
Na
þ
and
K
þ
Na
þ
current rises to a
peak first and then returns to zero as the clamp voltage is maintained. The
channel resistances are engaged and follow a typical profile. The
K
þ
current falls
Na
þ
current peaks and is maintained at this level
until the clamp voltage is removed. This general pattern holds for both currents for all
clamp voltages above threshold.
The
to a steady-state current well after the
K
þ
channel resistance or conductance is easily determined by applying
Ohm's law to the circuit in Figure 12.20 and the current waveforms in Figure 12.21:
I
K
¼
V
m
E
K
R
K
Na
þ
and
¼
G
K
V
m
E
K
ð
Þ
ð
12
:
39
Þ
I
Na
¼
E
Na
V
m
R
Na
¼
G
Na
E
Na
V
m
ð
Þ
ð
12
:
40
Þ
These conductances are plotted as a function of clamp voltages ranging from
50 mV to
þ
20 mV in Figure 12.26.
For all clamp voltages above threshold, the rate of onset for opening
Na
þ
channels is
K
þ
channels, and the
Na
þ
channels close after a period of time, while
more rapid than for
0.0015
0.001
Na
0.0005
0
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.01
−
0.0005
K
−
0.001
Time (s)
FIGURE 12.25
Diagram illustrating sodium and potassium currents due to a 20 mV voltage clamp.
