Biomedical Engineering Reference
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gA
Alm
0.32
0.32
0.30
0.30
1st
2nd
1st
2nd
0.28
0.28
6.4
6.8
7.2
7.6
6.4
6.8
7.2
7.6
r
LL
r
LL
Fig. 5.22
G
I
,
II
as a function of
r
LL
for
the gA channel (
left panel
) and Alm channel (
right panel
) in lipid bilayer energetics in the first-
and second-order of lipid screening, respectively. Here,
q
L
The reaction coordinate which was used in the plot of
/
q
M
=
0
.
0025
be assumed that the gA channel stability decreases with the increase of the bilayer
induced dissociation force, we conclude that
τ
∝
(
−
(
d
0
−
))
. Considering the
theoretical value of
F
dis
in Eq.
5.13
, this experimental channel lifetime relation with
the mismatch is supported by a previously presented derivation of gA channel lifetime
(Eq.
5.27
) in a continuum distribution of local energy traps [
85
] which is also borne
out elsewhere [
6
,
56
].
Another possibility is to use the traditional way of deriving lifetime, using the
relation presented in Eq.
5.13
. Slight differences in the bilayer thickness gA channel
length mismatch dependence of the theoretical trend of gA channel lifetime appear
to depend on whether we use the expression for
F
dis
from the screened Coulomb
model (
exp
l
) in the case when
c
0
is
assumed to be unchanged. In both of these cases the theoretical channel destabiliza-
tion increases (lifetime
τ
th
decreases) exponentially at small values of
d
0
−
∼
exp
(
d
0
−
l
)), or the elastic bilayer model (
∼
(
d
0
−
l
)
l
but as
d
0
−
l
increases, higher channel destabilization is observed in the former case com-
pared to the latter case (see Fig.
5.24
). For any constant thermodynamic condition,
the average channel lifetime therefore changes as a negative exponential function
(or more strongly) of the hydrophobic mismatch between the bilayer thickness and
channel length.
The origin of this difference is readily found if we expand the exponential expres-
sion (screened Coulomb model) in a power series as:
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