Biomedical Engineering Reference
In-Depth Information
N Channels
R
=1/G
R
= 1/G
R = 1/G
-
-
-
E
E
E
+
+
+
FIGURE 12.12
The equivalent circuit for
N
ion channels is a single resistor and battery.
represent resistance. Since the conductances (channels) are in parallel, the total conductance
is the total number of channels,
G
0
:
N
, times the conductance for each channel,
G
¼
N
G
0
It is usually more convenient to write the conductance as resistance
1
G
,
R
¼
measured in
ohms (
). An equivalent circuit for the channels for a single ion is now given as a resistor in
series with a battery, as shown in Figure 12.12.
Conductance is related to membrane permeability, but they are not interchangeable in a
physiological sense. Conductance depends on the state of the membrane, varies with ion con-
centration, and is proportional to the flow of ions through a membrane. Permeability describes
the state of the membrane for a particular ion. Consider the case in which there are no ions on
either side of the membrane. No matter how many channels are open, G
O
0 because there are
no ions available to flow across the cell membrane (due to a potential difference). At the same
time, ion permeability is constant and determined by the state of the membrane.
¼
Equivalent Circuit for Three Ions
Each of the three ions
Cl
are represented by the same equivalent circuit,
as shown in Figure 12.12, with Nernst potentials and appropriate resistances. Combining
the three equivalent circuits into one circuit with the extracellular fluid and cytoplasm
connected by short circuits completely describes a membrane at rest (Figure 12.13).
K
þ
,
Na
þ
, and
Outside
R
Na
R
K
R
Cl
V
m
-
-
-
E
Na
E
K
E
Cl
+
+
+
Inside
FIGURE 12.13
Model of the passive channels for a small area of nerve at rest, with each ion channel repre-
sented by a resistor in series with a battery.
