Biomedical Engineering Reference
In-Depth Information
The number of channels in a lipid bilayer can therefore be derived by
measuring the bulk solution conductivity and calculating the conductance of the
bilayer, given by the slope of the
I-V
plot. As an example, in the case of 0.5 M
NaCl,
s
b; NaCl
is 44.6
mS cm
1
. Using equation (
4.2
),
G
c; NaCl
is calculated to
be 1.72 nS. As noted earlier,
N ¼
G
m
G
c
0.92. The
calculated values for channel conductance (from the derived equations) are in
good agreement with the values obtained by means of current jump under the
same solution conditions.
. Using
G
m
¼
1.59 nS, gives
N ¼
4.4.5 Calculating the Calibration Coefficient for the KCl
and NaCl Buffer
The slopes ratios from experiments with KCl and NaCl were calculated under
the same number of connector insertions. With 0.5 M, 1.0 M, 1.5 M and 2.0 M
KCl and NaCl solutions, the slope ratios of KCl to NaCl were 1.50, 1.71, 1.67 and
1.70, respectively. The average value of 1.65 can then be used as a calibration
coefficient for translating the conductance calculated from buffers with K
+
to Na
+
as follows:
G
m; KCl
¼ F N G
c; NaCl
(4.4)
where
G
m; KCl
and
G
c; NaCl
are the single channel conductance in the same concen-
tration of KCl and NaCl respectively;
F
is the calibration coefficient for the KCl and
NaCl salt solutions. The same equation can be applied to approximate the conduc-
tance induced by multiple connector channels under the same buffer conditions
with different conducting ions, such as K
+
, as long as the single channel conduc-
tance in NaCl solution is known.
4.4.6 Comparison of Phi29 Connector Channel Conductance
with
a
-Hemolysin
The diameter of the narrow end of the connector channel is 3.6 nm, while the
channel formed by
-HL has a diameter of only 1.5 nm [
49
]. The ratio of the cross-
sectional area of the connector and
a
-HL channels is calculated to be 5.7. The ratio
of measured conductance of the connector to
a
-HL is 5.1 (Table
4.2
). Since
the conductance of a channel is proportional to its cross-sectional area, it can
therefore be concluded that the cross-sectional area of the connector in the buffer
solutions was approximately 5.1-fold greater than that of
a
-HL, which compares
well with the ratio of cross-sectional areas from the crystal data of both proteins.
a
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