Biomedical Engineering Reference
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dimer monomer
λ
+
dimer
G
‡
Δ
λ
monomer
Fig. 5.5
Chemical kinetics illustration of the back-and-forth transitions between gramicidin A
dimer (D) and monomer (M) states. The monomers in the far left energy well are bound to each
other, but the monomers in the far right energy well are free from each other. The back-and-forth tran-
sition between dimer and monomer states happens near the central energy state. The gramicidin A
monomer has been schematically shown as a block. As to the role of the energy state representing
the left-most energy well, the contribution of the central energetic barrier with barrier height
G
‡
(
vertical double arrow
) relative to the energy well representing the dimer state is very important
for the stability of the gramicidin A dimer ( channel) state. The dissociation between the monomers
may happen due to linear displacement, rotational bending, etc. To easily understand the problem,
we analyze the dissociation mechanism here using only the linear displacement of the monomers
along the channel length
where
H
B
,
H
X
and
H
C
are phenomenological elastic constants, depending mainly on
the bilayer elastic properties, namely compression and bending moduli (for details see
[
13
]). In this elastic model, the bilayer deformation free energy has been calculated
based on the original proposal that for small deformations, the free energy consists
of a layer-compression term, a splay-distortion term, and a surface-tension term,
equivalent to the elastic free energy of a two-layer smectic liquid crystal with surface
tension [
40
]. Consequently,
F
dis
follows a linear relationship with respect to (
d
0
−
l
)
and
c
0
[
6
,
13
] such that
G
def
∂
F
dis
=−
−
)
=
2
H
B
·
(
d
0
−
l
)
+
H
X
·
c
0
.
(5.12)
∂(
d
0
−
l
Increasing (
d
0
−
l
) and/or
c
0
leads to an increase in
F
dis
which causes destabilization
of gramicidin A channels following this general relation between
F
dis
and gramicidin
A channel lifetime via the bilayer deformation energy contributions:
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