Lipid Bilayer-Membrane Protein Coupling - Membrane Biophysics, Biological and Medical Physics, Biomedical Engineering - page 118

the channel length or increasing the bilayer thickness. The experimental results fit
perfectly with the trends found in the theoretical model. A shorter gramicidin A
channel (gA-(13)) is experimentally observed to be less stable than a longer grami-
cidin A channel (AgA(15)), or both of these channels are exponentially less stable
in a thicker (DC 20 : 1 PC) bilayer than in a thinner (DC 18 : 1 PC) one. Other important
parameters in the theoretical model are the intrinsic lipid curvature and the lipid
charge. An increased effective lipid cross-sectional area is a result of either a higher
negative curvature, e.g. PE's over PC's, or the lipid head group charges causing
Coulomb repulsion between lipids. The model calculation shows that increased lipid
cross-sectional areas (

r LL ) result in a modest increase in G I , II , which makes

the channel formation harder so the lifetime of a channel decreases. The experimen-
tal results show that gramicidin A channel lifetimes in a negative curvature-bearing
DOPE bilayer are shorter than those in a neutral DC 18 : 1 PC bilayer: the effect of neg-
ative curvature induces linear destabilization in gramicidin A channels. As the value
of r LL increases with the increase in lipid intrinsic curvature, we conclude that a very
good agreement exists between the theoretical predictions and experimental obser-
vations. Using the theoretical expression for the channel-bilayer binding energy, one
can also derive the elastic force constants and consider higher order effects on elastic
force constants with an increased value of s (representing a higher mismatch) exactly
illustrating the effects of lipid charges, as shown in Eq. 5.29 . Thus, an increased
bilayer elasticity helps the bilayer to deform near the channels. Despite elasticity
effects being secondary relative to the charge effects, the increased bilayer elasticity
reduces the bilayer deformation energy which favors the stability of a channel in a
bilayer membrane. Higher values of s , corresponding to a higher mismatch d 0 −

∼

l ,

also indirectly confirm that an equal increase in bilayer elasticity reduces G I , II

for shorter gramicidin A channels (accounting for a larger mismatch) more than that
for longer gramicidin A channels (accounting for a smaller mismatch). As a result,
stability of shorter gramicidin A channels increases relatively more strongly than
that of longer gramicidin A channels. The experimental studies [ 10 , 11 , 13 ] claimed
to induce increased elasticity into bilayers by bilayer-active amphipathic molecules,
such as several anti-fusion peptides, amphiphiles like triton X-100 and capsaicin, and
even an antimicrobial peptide gramicidin S. They also demonstrated that channels
generally show higher stability with an increase of the elasticity of the lipid bilayers.
Furthermore, in [ 13 ] it was shown that by increasing bilayer elasticity, the bilayer
deformation energy is reduced which in the model calculation appears as a decrease
in

G I , II . Requirements of higher gramicidin A and alamethicin concentrations in
both thicker bilayers and more negative-curvature bearing PE bilayers over PC bilay-
ers also confirm that a higher mismatch between the bilayer's hydrophobic thickness
and channel length and negative lipid curvature are two very important regulators
of channel functions, which the theoretical model predicts and experimental results
confirm.
In this chapter, we have developed a theoretical model for bilayer channel ener-
getics based on experimentally measurable values of general physical properties,
such as charge and size of the channel-forming peptides and the bilayer con-
stituents e.g. mainly lipids. By considering a simple model of screened Coulomb