Biomedical Engineering Reference
In-Depth Information
chapter, we also investigate the functions of another structurally different channel
produced by alamethicin peptides.
We have learned earlier that the gramicidin A channel is a linear dimer. The
atomic resolution structure of this channel is well-established, with the channels
being dimers of two right-handed, β
3 -helical subunits [ 8 , 46 , 86 ]. The bilayer-
spanning channels are formed by the reversible, trans-bilayer association of these
β
6
.
6 . 3 -helical monomers [ 68 ]:
k 1
k 1 D
M left +
M right
,
(5.6)
where M and D denote gramicidin A monomers and dimers, respectively, and the
subscripts denote monomers residing in each bilayer leaflet. Here, k 1 and k
1 are
2 ; with
two rate constants determining the channel appearance rate ( f gA =
k 1 ·[
M
]
[
being the gramicidin A monomer concentration) and gramicidin A channel
lifetime ( τ =
M
]
k 1 ). Within limits, the channel structure is invariant when the
lipid bilayer thickness is varied [ 45 , 89 ], meaning that the gramicidin A channels
are more rigid than the host bilayer. Consequently, when the bilayer's hydrophobic
thickness is larger than the channel's hydrophobic length, as is the present case, the
bilayer will adjust locally to match the channel length, which incurs an energetic cost
corresponding to the bilayer deformation energy
1
/
G def . When a channel disappears,
a transition state is reached when two of the six H-bonds that stabilize the bilayer-
spanning dimer are broken [ 26 , 61 ], in which case the two subunits have moved
a distance λ +
0Å)
of the bonds attaching two gramicidin A monomers in a gramicidin A dimer. The
movement of the two subunits relative to each other is very complex, involving both
a rotation and a lateral axial displacement [ 61 ]. For simplicity, here we focus on just
the linear gramicidin A association/dissociation mechanism only.
Changes in
, which may be slightly greater than the average length λ (
1
.
G def will shift the equilibrium distribution between non-conducting
gramicidin A monomers and conducting channels. Using Eq. 5.5 , the dimerization
constant for gramicidin A channel formation, K D , is found as
exp
G prot +
G def
[
D
]
k 1
k 1 =
K D =
=
,
(5.7)
2
[
M
]
k B T
G prot denotes the energetic contributions due to the channel subunit-subunit
interactions. Here,
where
is the concentration of dimeric gramicidin A channels.
Because bilayer deformation energy
[
D
]
G def varies as a function of the mismatch
between the bilayer thickness and the gramicidin A channel length
,the
bilayer responds to the deformation by imposing a disjoining force on the bilayer-
spanning channels:
(
d 0
l
)
G def
r
F dis =−
.
(5.8)
 
 
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