Biomedical Engineering Reference
In-Depth Information
Log
[
Δ
G
I,II
]/
free unit
10
18
240000
Ad hoc
assumption
10
13
200000
10
8
160000
120000
10
3
80000
10
-2
15
20
25
30
35
40
(
d
0
-
l
)/2
sec
δ /
Å
Fig. 5.23
sec
δ
is the distance covered
by the lipid head groups in the deformed regions of the bilayer at the bilayer gA channel interaction
sites.
δ
(for simplicity, they can be assumed to appear with a constant value within 0
Plot of Log[
G
I
,
II
] as a function of
d
0
−
l
. Here,
(
d
0
−
l
)
90
◦
in a
particular lipid bilayer membrane for all participating lipids in all orders of screening at the gA
channel bilayer interface), the angle at which lipids in the deformed portion of the bilayer couple
with the extension of the gA channel length.
−
G
I
,
II
increases exponentially with
d
0
−
l
.
G
I
,
II
at
lower values of
d
0
−
l
(e.g.,
d
0
−
l
≈
0 ) or at other higher values of
d
0
−
l
can be extrapolated from
the plot. For a certain type of lipid with a fixed lipid charge,
. Consequently,
the dissociation force imposed by the bilayer on the gA channel (
F
dis
) increases exponentially
with
d
0
−
l
, i.e.,
F
dis
G
I
,
II
∝
exp
(
d
0
−
l
)
∂
G
I
,
II
(
d
0
−
l
)
∂(
d
0
−
l
)
∝
exp
(
d
0
−
l
)
. As a result, the gA channel lifetime
decreases exponentially with the increase of
d
0
=−
−
−
l
.
Ad hoc
assumptions (
q
gA
∼
electron charge
and other relevant parameters [
1
,
16
,
17
,
35
,
41
,
71
,
75
] give an estimate of
G
I
,
II
/ (kJ/mole)
which strongly depends on
q
L
as
d
0
increases. Results in previous figure fall within the second-order
screening (
d
0
40 Å). Experimentally, this was observed in previously published data [
6
,
56
]
and here in the experimental results section
−
l
<
1
2
3
4
(
d
0
−
l
)
)
+
(
d
0
−
1
)
+
(
d
0
−
1
)
e
(
d
0
−
l
)
=
G
I
,
II
=
+
+
(
d
0
−
1
+
...
2
6
24
=
G
I
,
II
(
Harm
)
+
G
I
,
II
(
A.Harm
).
(5.33)
The symbols Harm and A.Harm denote the harmonic and anharmonic contribu-
tions in
G
I
,
II
, respectively. The necessity to include
G
I
,
II
(A.Harm) is gener-
ally expected in the case with higher values of
d
0
−
l
(see Fig.
5.2
1) whereas the
elastic bilayer theory predicts the presence of only a harmonic term
2
in
the bilayer deformation energy, which is adequate for sufficiently small deformation
values. This is also readily found in the screened Coulomb energy. Consequently,
F
dis
=
∼
(
d
0
−
l
)
∂
G
I
,
II
in the screened Coulomb model also contains additional terms
(different orders) besides the term (
d
0
−
)
∂(
d
0
−
l
l
), which is the only geometric mismatch
term found in the elastic bilayer theory to regulate the change of the gA channel
lifetime (in the case of non-changing lipid curvature profiles). Although both the
screened Coulomb model and the elastic bilayer model calculations generally sug-
gest an exponential damping in gA channel lifetime with increasing
d
0
−
l
which
is consistent with the experimental data presented in Sect.
5.4
(and in [
6
,
56
]), the
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