Shape and Phase Transitions in a PEGylated Phospholipid System

Poly(ethylene glycol) (PEG) polymers and PEG-conjugated lipids are widely used in bioengineering and drug transport applications. A PEG layer in a drug carrier increases hydrophilic repulsion, inhibits membrane fusion and serum opsonin interactions, and prolongs the storage and circulation time. It can also change the carrier shape and have an influence on many properties related to the content release of the carrier. In this paper, we focus on the physicochemical effects of PEGylation in the lipid bilayer. We introduce laurdanC as a fluorophore for shape recognition and phase transition detection. Together with laurdanC, cryogenic transmission electron microscopy, differential scanning calorimetry, molecular dynamics simulations, and small-angle X-ray scattering/wide-angle X-ray scattering, we acquire information of the particle/bilayer morphology and phase behavior in systems containing 1,2-dipalmitoyl-sn-glycero-3-phosphocholine:1,2-distearoyl-sn-glycero-3-phosphoethanolamine-PEG(2000) with different fractions. We find that PEGylation leads to two important and potentially usable features of the system. (1) Spherical vesicles present a window of elevated chain-melting temperatures and (2) lipid packing shape-controlled liposome-to-bicelle transition. The first finding is significant for targets requiring multiple release sequences and the second enables tuning the release by composition and the PEG polymer length. Besides drug delivery systems, the findings can be used in other smart soft materials with trigger-polymers as well.


Core Shell Structure
The core-shell structures of liposomes and bicelles are presented in in Scheme 1. The entire structure is shown on the left and the component layers on the right. Each component layer i contains a factor ± i Δ i w i , where i is its volume, i its form factor amplitude, and Δ i w = i − 0 its scattering length density (SLD) in contrast with water ( 0 is the SLD of water).

Scheme 1.
A: The core-shell structure of a liposome. On the left, the full representation; on the right, its divisions into component layers. B and C are two cylidrical core-shell structures with three layers (1, core; 2, face; and 3, rim). D represent a bicelle.
For a liposome (Scheme 1A), the component layers are 1) water, 2) the inner lipid head groups, 3) the lipid tail groups, and 4) the outer lipid head groups. These have spherical symmetry, characterized by the Rayleigh form factor amplitude 1 i = 3(sin i − i cos i )( i ) −3 that shows strong oscillation in the measurable range.
In a real system, polydispersity of the particles attenuates the oscillation. This can be taken into account with a Gaussian weight coefficient j ( j ) = (√2 PDI • 1 ) −1 exp (− j 2 (√2PDI • 1 ) −2 ) , where PDI is the polydispersity index, 1 is the radius of the water phase, and j is the deflection length that belongs to a group j ∈ { | ∈ ℝ, | | ≤ 3PDI • 1 }. The idea is that each layer is deflected by j , so that i,j = i + j and the volume where Δ i = i−1 − i is the layer contrast with 4 = 0 and 1 = 3 , because the lipid head groups are assumed self-similar.
The bicelle core was modelled as a combination of structures shown in Schemes 1B and 1C. The resulting structure is shown in Scheme 1D.

S3
The form factor amplitude of a cylinder is given by Fournet 5 : i = J 1 ( i sin ) sin( i cos ) ( 2 i i sin cos ) −1 , where is the angle between the incident beam and the cylinder normal, J 1 is the modified Bessel function of order 1, and i and i are the half-thickness and the radius of the i th component layer. When the weighted polydispersity coefficient with the deflected radius i,j and the volume i,j = 4 i,j (S2) Table S1 shows the SAXS fit parameters used in the fit in Figure 2.

Molecular Dynamics Simulations: additional details System Setup and Model Details in 10500 lipid systems
For the DPPC and DSPE lipids, the DRY-MARTINI coarse-grained beads and parameters follow Ref. 6   The bonded parameters (bonds, angles, torsions) have been obtained by fitting the resulting bond, angle, and dihedral distributions to reproduce the corresponding data sets obtained from atomistic simulations. 9, 10 Except for the torsions which use the CBT potential which enables longer simulation time step, 11 the bonded parameters correspond to harmonic functions. The non-bonded parameters, i.e. Lennard-Jones parameters, follow the octanol-water partition energies presented in Ref. 6 . The PEG self-interaction was tuned to reproduce PEG RG in solution, following Refs. 9

Matlab Script for the Cryo-TEM Analyses
This Matlab script is used to analyze cryo-TEM images. The script is used as follows: 1) run the script, 2) select the TEM image file(s), 3) click "Next Sample" to present the first image, 4) set the pixel size value according to your TEM image, 5) press "Add" to mark particulates, 6) adjust the zoom first and then click enter to start selecting particles; click the circumferential edges across the particle to obtain their size, 7) press enter when finished, 8) press "Remove" if you need to remove a miss-selection, 9) press "Save" to generate a txt data file, 10) press "Next Sample" to open the next TEM image; "Next Sample" displays a histogram if used for the last image.