Biomedical Engineering Reference
In-Depth Information
Fig. 5.7
Gramicidin A monomer (gA) in a channel is assumed to find a lipid (just the head group
is schematically shown) on the perturbed region of the bilayer next to it with a bare Coulomb
interaction, but the next-neighboring lipid with the first-order screened Coulomb interaction, and
so on. The gA monomer can no longer extend its interaction beyond the lipid on the right side of
the downward pointing arrow where the bilayer regains the form of its unperturbed thickness. Here,
we have shown only they are mainly because most probably they are mainly responsible for the
effective localized charges in lipids
where the Lennard-Jones potential between the two gramicidin A monomers is
given by
∂
∂
2
U
∂
r
2
3
U
∂
r
3
1
2
2
1
6
)
=
r
∗
)
+
r
∗
)
r
∗
)
3
U
LJ
(
r
U
LJ
(
r
∗
(
r
−
r
∗
(
r
−
r
=
r
=
∂
4
U
∂
r
4
1
24
r
∗
)
4
+
r
=
r
∗
(
−
+
...
r
(5.17)
r
∗
)
+
A
(
r
∗
)
B
(
r
∗
)
C
(
r
∗
)
2
3
4
U
LJ
(
r
−
+
r
−
+
r
−
+
...,
where
r
∗
≈
average length of a hydrogen bond.
The Coulomb interaction between the two gramicidin A monomers is given by
q
gA
4
π
0
r
r
.
U
coulomb
(
r
)
=
(5.18)
The formation of a gramicidin A channel due to dimerization of two monomers
inside lipid membranes is a well-studied issue. The way in which the presence of
the ordered matrix of a lipid bilayer ensures the membrane-associated gramicidin A
structure was already thoroughly addressed in an investigation some three decades
ago [
89
]. The strong binding involving two gramicidin A monomers with identical
charges is supported by an earlier work on the derivation of an effective attrac-
tive interaction potential between charges of the same type in solution [
32
]. In this
chapter, the primary goal is to investigate the effect of hydrophobic bilayer thick-
ness channel length mismatch on the stability of the already formed gramicidin A
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