Impact of poly(ethylene glycol) functionalized lipids on ordering and fluidity of colloid supported lipid bilayers

Colloid supported lipid bilayers (CSLBs) are highly appealing building blocks for functional colloids. In this contribution, we critically evaluate the impact on lipid ordering and CSLB fluidity of inserted additives. We focus on poly(ethylene glycol) (PEG) bearing lipids, which are commonly introduced to promote colloidal stability. We investigate whether their effect on the CSLB is related to the incorporated amount and chemical nature of the lipid anchor. To this end, CSLBs were prepared from lipids with a low or high melting temperature (Tm), DOPC, and DPPC, respectively. Samples were supplemented with either 0, 5 or 10 mol% of either a low or high Tm PEGylated lipid, DOPE-PEG2000 or DSPE-PEG2000, respectively. Lipid ordering was probed via differential scanning calorimetry and fluidity by fluorescence recovery after photobleaching. We find that up to 5 mol% of either PEGylated lipids could be incorporated into both membranes without any pronounced effects. However, the fluorescence recovery of the liquid-like DOPC membrane was markedly decelerated upon incorporating 10 mol% of either PEGylated lipids, whilst insertion of the anchoring lipids (DOPE and DSPE without PEG2000) had no detectable impact. Therefore, we conclude that the amount of incorporated PEG stabilizer, not the chemical nature of the lipid anchor, should be tuned carefully to achieve sufficient colloidal stability without compromising the membrane dynamics. These findings offer guidance for the experimental design of studies using CSLBs, such as those focusing on the consequences of intra- and inter-particle inhomogeneities for multivalent binding and the impact of additive mobility on superselectivity.

. Different chemical units modelled as lattice beads in SCFT as well as their Flory-Huggins interaction parameter , relative permeabilities and charge per bead .
All beads occupy a single lattice site, except for PO which takes 5 lattice units in a crosslike shape. The two values of N arise from the fact that in DOPC N is positively charged, while in DSPE-PEG 2000 it is neutralized. Table S2. SCFT computed equilibrium properties of self-assembled SUVs modelled as   bilayers from the unimers specified: aggregation number  , bulk unimer concentration   (SCFT-provided cmc,  ), and gyration ( ) and hydrodynamic ( ) diameters.

S1. Preparation of silica particles
Silica particles of 3 µm were purchased from Micromod GmbH and washed 10 times with milli-Q water by centrifuging and redispersion to remove the storage buffer. Scanning electron microscopy (SEM) imaging found the particles to be spherical and monodisperse with an average diameter of 3.24 ± 0.12 µm ( Figure S1). Figure S1. SEM image of purchased 3 µm silica particles.

S6. Self-consistent mean-field theory (SCFT) predications of the composition of colloid supported lipid bilayers
The self-consistent mean-field theory (SCFT) employed to model phospholipid self-assembly follows the lattice discretization scheme by Scheutjens and Fleer. [1][2][3] SCFT is a predictive tool for self-assembly of amphiphiles and has been applied to systems ranging from block copolymers to surfactants. [4][5][6] The principle characteristic followed by SCFT to study selfassembly is the grand potential Ω, associated with inhomogeneities in the system of interest, held in equilibrium with the bulk solution. [7,8] SCFT is based upon Flory-Huggins (FH) theory, with first-order Markov chain statistics for the conformations of all the compounds involved. [9] Importantly, in order to optimize the free energy of the relative amounts of the compounds in solution, each chemical unit and their respective interactions are defined via the FH interaction parameters.
The equilibrium properties of self-assembled species are resolved by coupling SCFT with the thermodynamics of small systems. [7] A thermodynamically stable self-assembly is found SCFT is employed here to study the properties of vesicles resulting of mixing two different lipids, DOPC and DSPE-PEG 2000 , hence following a co-assembly process. In this case, the impact that a given number of a second compound has on the -curve of the single lipid 2 Ω 1 case, is shown in Figure S6. self-assembly. [5,11] Each chemical unit is considered as taking up a single lattice unit, except for the phosphate group which takes five units arranged in a cross-like shape ( Figure S7). To account for electrostatic interactions, the lattice site size b needs to be specified, as well as the relative permeabilities of the different chemical units considered. Here we set nm. concentration gradients in one direction. [12] Hence all local concentration profiles of the molecules involved are allowed to vary in the z-direction, while the concentrations in other directions are identical. The set of molecular parameters is schematized in Figure S7. Below we provided the modelling parameters used for the SCFT computations. In Table   S1 the FH interaction parameters , relative permeabilities and number of charges per monomer considered for the different chemical units defined as lattice beads. We also provide the SCFT phospholipid structures used, as it further clarifies the coarse-graining conducted. The software sfbox was used to perform SCFT computations. sfbox input files and templates are available from dr. Álvaro González García upon reasonable request, as well as the Mathematica scripts used in the data processing of the output files. [13] Below we provide more detailed SCFT results on the phospholipid bilayers used to model the vesicles studied experimentally. In Table S2 we summarize several equilibrium properties of the systems studied, as computed using SCFT. . This follows from the fact that PEG is water-soluble, therefore the bilayer-bulk equilibrium shifts to the bulk upon PEGylation.
The thermodynamics of mixed lipid vesicle formation are summarized in Figure S5  . As observed in Figure S8a, the amount of DOPC in the self-

S6. Atomic force microscopy on planar supported lipid bilayers
Circular mica substrates glued on Teflon discs were used for the atomic force microscopy

S7. Differential Scanning Calorimetry
Calorimetric studies were carried out using a Multi-Cell micro-DSC (TA Instruments). Samples (~8 mM of SUV or CSLB) were dispensed into pre-calibrated sample cells, cell 1 and cell 2, with an approximant weight of 400 mg. Buffer solution (~400 mg) was added to cell 3, allowing heating and cooling scans of samples with buffer to be completed simultaneously.
Additionally, cell 4 remained empty for reference of the crucible. A scan heating rate and cooling rate of 0.5 °C /min and 1 °C /min were used for all samples, respectively.
Sample runs were performed in the temperature range between 10 °C and 80 °C and repeated in technical triplicate to ensure the closeness of successive measurements within the same conditions. Each heating and cooling scan was than examined using NanoAnalyze Data Analysis (Version 3.11.0, www.tainstruments.com) to determine the accuracy of the measured value (T m ) and true value reported in literature ( Figure S10). Initially, the background was subtracted from raw sample data in μJ/s and converted to molar heat capacity by volumes (moles). In order to exclude initial heating/ cooling ramps (artifacts introduced by instrument), analysis on data was completed between the ranges of 25 °C and 55 °C were selected for baseline correction (20-60 °C heating, for DPPC only). The baseline of raw data was constructed via sigmoidal baseline fitting, followed by Gaussian fitting models to ascertain T m and FWHM. Models were fitted for a maximum 100000 iterations with a fitting precision of 1×10 -6 and statistics completed at 1000 trails at 95% confidence level. All measurements were conducted at 20 °C in 1 cm path-length borosilicate disposable tubes.
All solvents were filtered using a 0.2 µm filter. For each measurement the viscosity was corrected for any change in temperature during measurements. Figure S12. Dynamic light scattering curves at 90° of DPPC and DOPC SUV samples with 10%DSPE-PEG incorporated into membrane.