C. Position of an Isolated Fullerene within the Lipid
Bilayer. Figure 5 shows the free energy (POMF) of the lipid
bilayer/single fullerene system as a function of the position of
the center-of-mass of the fullerene relative to the center-of-mass
of the lipid bilayer. In contrast to small hydrophobic solutes,
the large C
60
fullerene prefers to be situated off of the center
plane. As show in Figure 2, the atomic density within the bilayer
is lowest at the center layer and increases toward the head group
layer. Favorable dispersion interactions between the atomically
dense surface of the fullerene and its environment (e.g., see
Figure 3) result in a migration of the fullerene toward the denser
region of the bilayer. As shown in Figure 2, a fullerene C
the most favorable interaction (Lennard-Jones energy) with its
surroundings at a position of 10-15 Å from the bilayer center.
However, the minimum in the POMF is around position of 6-7
Å. Moreover, the free energy steeply increases as C
fullerene
moves more than 8 Å from the center of the bilayer despite the
favorable nonbonded interaction with surrounding. This mismatch
in position of the minima for the energy and the free
energy can be explained by distortion of the bilayer. For
positions larger than 8 Å away from the center of the bilayer
the fullerene begins to penetrate into the more structured head
group region causing significant structural distortion. The latter
is illustrated in Figure 6, where the relative position of head
groups for lipids, which are located near the fullerene, is
compared to the position of head groups of neighboring lipids.
Specifically, we have defined a cylinder of radius R
which is normal to the lipid bilayer and with an axis going
through the fullerene center-of-mass as schematically shown
on the inset of Figure 6. Then, the average of head group
positions (defined by phosphorus atoms), which are inside the
cylinder and are located in the same half of the lipid bilayer
(upper or lower) as the fullerene, was calculated (〈Z
average position was compared with the average position of
head groups of neighboring lipids (〈Z
〉), which are located
inside of a larger cylinder R
2
h2
) 11 Å but outside of the smaller
cylinder. ¢Z
h
) 〈Z
h1
〉 - 〈Z
〉 as a function of fullerene position
in the lipid bilayer is shown in the main panel of Figure 6. It
can be clearly seen that penetration of the fullerene inside the
bilayer tails by more than 8 Å away from the bilayer center-ofmass
results in displacement of nearby head groups by as much
as 2 Å relatively to other lipids. This displacement can
noticeably disrupt the lipid-lipid interactions and hence be
energetically unfavorable. Therefore, the observed preferred
position for the fullerene shown in Figure 5 reflects not only
fullerene-bilayer interaction energy but also additional factors
such as distortion of the DMPC structure and disturbance of
hydrogen-bonding structure in the DMPC head group region.
C. Position of an Isolated Fullerene within the LipidBilayer. Figure 5 shows the free energy (POMF) of the lipidbilayer/single fullerene system as a function of the position ofthe center-of-mass of the fullerene relative to the center-of-massof the lipid bilayer. In contrast to small hydrophobic solutes,the large C60fullerene prefers to be situated off of the centerplane. As show in Figure 2, the atomic density within the bilayeris lowest at the center layer and increases toward the head grouplayer. Favorable dispersion interactions between the atomicallydense surface of the fullerene and its environment (e.g., seeFigure 3) result in a migration of the fullerene toward the denserregion of the bilayer. As shown in Figure 2, a fullerene Cthe most favorable interaction (Lennard-Jones energy) with itssurroundings at a position of 10-15 Å from the bilayer center.However, the minimum in the POMF is around position of 6-7Å. Moreover, the free energy steeply increases as Cfullerenemoves more than 8 Å from the center of the bilayer despite thefavorable nonbonded interaction with surrounding. This mismatchin position of the minima for the energy and the freeenergy can be explained by distortion of the bilayer. Forpositions larger than 8 Å away from the center of the bilayerthe fullerene begins to penetrate into the more structured headgroup region causing significant structural distortion. The latteris illustrated in Figure 6, where the relative position of headgroups for lipids, which are located near the fullerene, iscompared to the position of head groups of neighboring lipids.Specifically, we have defined a cylinder of radius Rwhich is normal to the lipid bilayer and with an axis goingthrough the fullerene center-of-mass as schematically shownon the inset of Figure 6. Then, the average of head grouppositions (defined by phosphorus atoms), which are inside thecylinder and are located in the same half of the lipid bilayer(upper or lower) as the fullerene, was calculated (〈Zaverage position was compared with the average position ofhead groups of neighboring lipids (〈Z〉), which are locatedinside of a larger cylinder R2h2) 11 Å but outside of the smallercylinder. ¢Zh) 〈Zh1〉 - 〈Z〉 as a function of fullerene positionin the lipid bilayer is shown in the main panel of Figure 6. Itcan be clearly seen that penetration of the fullerene inside thebilayer tails by more than 8 Å away from the bilayer center-ofmassresults in displacement of nearby head groups by as muchas 2 Å relatively to other lipids. This displacement cannoticeably disrupt the lipid-lipid interactions and hence beenergetically unfavorable. Therefore, the observed preferredposition for the fullerene shown in Figure 5 reflects not onlyfullerene-bilayer interaction energy but also additional factorssuch as distortion of the DMPC structure and disturbance ofhydrogen-bonding structure in the DMPC head group region.
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