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of considerable Alm channel activity under the experimental conditions, a minimum
of 10
−
8
) is required in
DC
18
:
1
PC
/
n
-decane
bilayers [
12
]. However, once the Alm channel starts showing, we observe that the
Alm channel activity increases considerably (reported in earlier observations to be
a power of 2.6 of the concentration at 25
◦
C[
51
]) as
M Alm peptide concentration (
[
M
Alm
]
increases. We also
observed that the Alm channel activity shows significant dependence on bilayer
thickness and on lipid curvature. Higher lipid charges also considerably destabilize
the probability of observing any Alm channel current level, especially higher order
current levels [
18
]. To observe comparable Alm channel activity (i.e., comparable
[
M
Alm
]
value of
i
r
i
=
i
(
(see Sect.
5.3.1
), where
A
i
and
A
nc
are the areas under
the peaks representing a current level
i
and the baseline in Alm channel current traces
as shown in Fig.
5.11
), about 10
−
8
Mof
A
i
/
A
nc
)
[
M
Alm
]
in
DC
18
:
1
PC
/
n
-decane bilayers was
10
−
7
M) of
required while 10-fold higher (
was required in DOPE/
n
-decane
very low probability of observing higher order current levels in bilayers formed with
DOPS lipids). On the other hand, a more than 10- or even 100-fold increase in the
concentration
∼
[
M
Alm
]
[
M
Alm
]
was required when
DC
18
:
1
PC
was replaced with
DC
20
:
1
PC
or
DC
22
:
1
PC
bilayers containing
n
-decane or squalene to observe comparable Alm
channel activity. The additional free energy (
G
nc
→
i
=−
k
B
T
ln
r
i
) (see earlier
section) involved in raising any current level in an Alm channel in thicker bilayers
or bilayers with higher amounts of negative curvature is perhaps compensated by
the requirement of a higher
[
92
]. Once comparable Alm channel activity is
observed, the relative probability of observing different Alm conductance levels e.g.,
j
[
M
Alm
]
W
j
(see Sect.
5.3.1
) in different bilayer system is also found to be
different, but does not vary within the same lipid system. The values of
W
2
/
+
k
and
jW
j
+
k
/
W
1
and
W
3
/
W
1
are observed to be 0
.
25
±
0
.
05 and 0
.
04
±
0
.
01 for
DC
18
:
1
PC
,1
.
38
±
0
.
21
and 0
.
88
±
0
.
21 for
DC
20
:
1
PC
,1
.
52
±
0
.
2 and 1
.
06
±
0
.
25 for
DC
22
:
1
PC
, and
2
0 for DOPE/
n
-decane bilayers. Consequently, the mean val-
ues of the changes in average free energies
.
05
±
0
.
8 and 2
.
23
±
1
.
G
1
→
2
G
1
→
3
are observed to be
and
−
0
.
6
k
B
T
and
−
1
.
39
k
B
T
for
DC
18
:
1
PC
,0
.
14
k
B
T
and
−
0
.
55
k
B
T
for
DC
20
:
1
PC
,
0
.
182
k
B
T
and 0
.
025
k
B
T
for
DC
22
:
1
PC
, and 0
.
31
k
B
T
and 0
.
35
k
B
T
for DOPE/
n
-
decane bilayers. The values of
W
2
/
W
1
and
W
3
/
W
1
are observed to be 0
.
21
±
0
.
15
G
1
→
2
and
G
1
→
3
are found to be
and 0
.
053
±
0
.
04, respectively. Consequently,
−
28
k
B
T
, respectively, in DOPS/
n
-decane bilayers with negligible
presence of current levels above the third current level.
0
.
68
k
B
T
and
−
1
.
5.5 Theoretical Results/Numerical Results Regarding the
Functions of Gramicidin A and Alamethicin Channels
Due to Their Coupling with Lipid Membranes
Based on the model of gA channels in lipid bilayers (see Fig.
5.2
) we deduce that
any gA channel exists in a lipid bilayer through bilayer deformations at the channel
bilayer interfaces to compensate for the hydrophobic mismatch (
d
0
−
l
) between
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