The interactions between CG PEG and CG lipid were parametrized by comparing conformations of PEG on the lipid bilayer from all-atom and CG simulations. Using this CG model, simulations show that mixtures of lipids and PEGylated lipids self-assemble to liposomes, bicelles, or micelles, with smaller aggregates at higher concentrations of PEGylated lipids. Similarly, experiments have shown that liposomes stably form up to 5~10 mol% DPPE-PEG45, bicelles start to form at ~10 mol%, and there are only small micelles at concentrations of more than 30–35 mol%.46,49
Although different experimental methods have shown slightly different concentrations for each phase,48
the simulated assemblies are consistent with these boundaries. Note that in experiment the formation of the bicelles and small liposomes respectively requires temperature change (heating and cooling between the transition temperature), and sonication.48
While these methodological differences highlight the approximate nature of the CG model, simulations still reproduce the trend for the experimentally observed phase behavior of PEGylated lipids at different concentrations of PEGylated lipids.
Simulations also show that PEGylation causes smaller aggregates for both liposomes and bicelles, but their effects differ. Different lengths of PEG12, PEG28, and PEG45 do not influence the bicelle size, while they do modulate liposome size. This appears to be related to the migration of the PEGylated lipids in the bicelles to the rim, while those in the liposome are distributed uniformly, as discussed below.
Simulated bicelles initially form with irregular ellipsoidal shapes, but equilibrate to circular disks (). This disk shape of the bicelle has been proposed50
and experimentally supported.51
A higher fraction of DPPE-PEG is observed at the edge than on the planar surface of the bicelle, in qualitative agreement with experimental observations using SANS.19
For the systems having the same charge density without PEG chains, DPPE-PEG0 are distributed uniformly on the bicelle surface, indicating that the component segregation of lipids at the planar surface and PEGylated lipids at the rim is caused by the PEG-induced bulky head group rather than by the repulsive electrostatic interactions between anionic lipid head groups. End-to-end distances of PEG45 on liposomes, bicelles, and micelles are also close to each other, and approximately 10% larger than obtain in water (). Hence, the aggregation state does not modulate the conformation of PEG with molecular weight of 2000 or less.
Although the present simulation results qualitatively agree with the experimental observation of the high DPPE-PEG concentration at the rim of bicelle, a substantial presence of PEG remains on the planar region ( and ). The thickness of the PEG layer at the surface of the fully-PEGylated micelle can be calculated using the brush theory for star-shaped polymers.52
From Vagberg et al.53
where L is the thickness of the PEG layer, N
is the number monomers per chain (e.g. 45 for PEG45), l
is the statistical length of the monomer (equivalent to the bond length of the CG bead, 3.3 Å), v
is the Flory exponent (3/5 for a good solvent), f
is the number of grafted chains (76 for the fully PEGylated micelle, as measured by static light scattering),54
is the radius of the micelle core (20 Å). The preceding formula yields L= 34 Å for PEG45. From , this is close to the end-to-end distance (<h2
) of a single PEG45 molecule in water calculated with the present CG model,26
though somewhat shorter than obtained here for a micelle, and other aggregates. These results imply that PEG45 is not long enough to adapt brush-like conformations on the fully-PEGylated micelle. A brush state of PEG on a bilayer has been observed in simulations26
(25–100 mol% PEG45) and X-ray diffraction experiments38
(10mol% PEG45), indicating that the high curvature of the micelle allows the PEG to adapt a disordered state.
Since PEG45 has the same length for different self-assembled structures, the PEG length calculated from Eq. (1)
for the fully-PEGylated micelle can be applied for PEG at the edge of the bicelle, as discussed above. However, longer PEG chains must be considered carefully. For example, <h2
= 56 Å for PEG113 (Mw
=5000) in water,26
while Eq. (1)
yields L=66 Å for the PEG113 grafted on the fully PEGylated micelle. The present simulations indicate that the ratio of DPPE-PEG45 to all lipids is 0.28–0.6 at the edge of the bicelle. It will be interesting to see if this result holds for longer PEG113 at the SANS-experiment concentration of 20 mol% DPPE-PEG113,19
and if Eq. (1)
is still applicable to bicelles.
In conclusion, the interactions between CG PEG and CG lipids were parametrized, and mixtures of lipids and PEGylated lipids in water were simulated at different sizes and concentrations of PEGylated lipids. Simulations capture the phase behavior of the self-assembled liposomes, bicelles, and micelles at different concentrations of PEGylated lipids, in qualitative agreement with experiment. PEGylated lipids are more concentrated at the rims of bicelles than at the planar surfaces, in agreement with experiment. However, the bicelle rim is not fully covered by PEG, and segregation is not complete. These findings imply that the bicelle rim should not be modeled as a fully-PEGylated micelle, and that PEGylated lipids in the planar region contribute to the effective hydrodynamic radius of the bicelle. The importance of these effects remains to be determined, and predictions of CG model must be tested both by experiment and more realistic simulations. Charged lipids without PEG evenly distribute at the rim and the planar surfaces of the bicelle, and form bicelles larger than those with PEGylated lipids. These differences are consistent with the notion that the bulky head groups with larger PEG induce more membrane curvature, which modulate the phase behavior and aggregate size.