Biomedical Engineering Reference
In-Depth Information
c
i
c
i+1
c
i+2
Fig. 5.9
The transition between different conduction pores of alamethicin channels
accounts for two such screened Coulomb interactions (see Eq.
5.14
). The interaction
between alamethicin monomers takes the form of the standard Coulomb energy
formula given below:
n
1
2
q
i
q
j
4
π
0
r
|
U
coulomb
(
r
)
=
r
j
|
.
(5.21)
r
i
−
i
=
j
If, for example, three monomers make the lowest conductance state in an alame-
thicin channel, we can assume that
|
r
i
−
r
j
|≈
r
. In the case of isotropic alame-
q
Alm
where
q
Alm
is the charge
on an alamethicin monomer. However, for other higher conductance states, where
the number of monomers involved is more than three, the distances between non-
adjacent monomers on each cylindrical alamethicin channel should be greater than
those between adjacent monomers. The term
U
LJ
(
thicin peptides, we can also assume that
q
i
q
j
≈
r
)
in alamethicin channels follows
an identical form to that in Eq.
5.17
.
5.3 Channel Energetics and Related Probabilities in the Context
of Channel Stability in Lipid Bilayers
We have discussed how we can generally apply the screened Coulomb interaction
model calculation for both gramicidin A and alamethicin channels. This qualifies
the model for general applications, which could involve the bilayer regulation of the
functions of membrane proteins with varied structures. Despite all indications of the
existence of identical bilayer membrane protein coupling energetics, the probabilities
emerging from different channel conformations require an independent treatment.
The gramicidin A channel's stability appears through its lifetime, which follows
Eq.
5.13
. That means the gramicidin A channel lifetime directly corresponds to the
strength of the bilayer channel energetic coupling. This concept is also partially
valid in the case of alamethicin channels and similar ones. As explained earlier,
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