Biomedical Engineering Reference
In-Depth Information
Fig. 5.3
Virtual springs (shown in
red
) are longitudinally attached to the two monolayers. For
simplicity of presentation we have shown that those virtual springs are attached with lipid head
group layers on each monolayer of the bilayer. The choice of the number and shape of the springs
is arbitrary
Fig. 5.4
A bilayer- integral gramicidin A channel coupling phenomenon is modeled here as a har-
monic interaction. Any gramicidin A channel is attached to a lipid monolayer with many imaginary
springs where any of these springs follows the motion of a harmonic oscillator following Eq.
5.2
.
Two gramicidin A monomers are attached to each other by hydrogen bonds and the monomer-
monomer separation falls within
λ
≈
1 Å or 0.1 nanometer (nm). To simplify the diagram we draw
two blocks representing two gramicidin A monomers in this figure instead of showing them as spiral
structures shown in Fig.
5.2
still be used as the main ingredient which causes the necessary energetic changes
required for this type of mechanical deformation.
Since both channel formation and channel breaking are statistical processes, the
geometrical adjustment of the free length
d
0
−
l
is a very temporary effect, but
certainly not instantaneous. The bilayer's elastic nature can help it to deform to
adjust with the channel's length so that a real physical binding between the lipid
layers and the channel's longitudinal edges may happen. In the case of gramicidin A
channels, we assume that if the channels try to extend linearly to compensate for the
mismatch
d
0
−
l
, the bonding at the center of the channel between two gramicidin
A monomers will be broken, so that the gramicidin A channels will themselves be
diluted into gramicidin A monomers. Instead, if the rather soft structured membrane
exhibits a deformation near the channel, the problem can be solved and gramicidin A
channels will show some stability. However, this requires a change of free energy due
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