To begin SCFT is used to predict the nature and strength of interactions (W) between SUVs and between CSLBs at equilibrium (ESI—Supplementary Section S1). (Li et al., 2009; Ianiro et al., 2018; González García et al., 2019; Ianiro et al., 2019; González García et al., 2020) As a representative case, the interaction between SUVs and between CSLBs composed of fluid lipid 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) with and without membrane additive poly (ethylene glycol) (PEG)-conjugated lipid 1,2-distearoyl-sn-glycero-3-phosphoethanolamine-N-[methoxy (polyethylene glycol)-2000] (DSPE-PEG₂₀₀₀) were predicted as a function of surface-to-surface distance (Figure 1). The interactions accounted for in the SCFT computations employed are direct interactions between all components quantified through Flory-Huggins parameters and electrostatic ones. The electrostatics are described using Gouy-Chapman equations (combining Boltzmann for the distribution of charges plus Poisson’s equation, see Ref 24 and ESI—Supplementary Section S1 for further information).

Negative W values indicate interparticle distances that give rise to attractive interactions, while overall positive values are characteristic for repulsive systems which can be considered colloidally stable. The interactions between DOPC SUVs (Figure 1A) were found to be repulsive within 10 nm proximity, regardless of the PEGylated lipid concentration. The overall repulsive interactions reflect the stability of the SUVs, which confirms what has been observed experimentally (Giakoumatos et al., 2022). Upon adding relatively more PEGylated lipids, the repulsive interaction becomes longer ranged and gets stronger (Figure 1A). Without PEGylated DSPE the repulsive interaction gets significant when the bilayers are less than 5 nm apart, while this distance increases upon adding more PEGylated DSPE. For 21% PEGylated DSPE it increases to almost 8 nm. Hence, the minimum proximity between DOPC SUVs can be seen to increase by a few nm upon addition of 2–21 mol% DSPE-PEG₂₀₀₀, obviously due to an additional steric repulsion mediated by the PEG₂₀₀₀ chains.

Interestingly, upon the formation of CSLBs by the rupture and fusion of DOPC bilayers onto the surface of silica spheres, an attractive well (see Figure 1B) appears at an interparticle distance of approximately 9 nm. This distance can be ascribed to the thickness of the bilayers on the respective silica spheres and suggests that DOPC CSLBs without DSPE-PEG₂₀₀₀ are prone to aggregation. An attractive contribution to the interaction between such lipid bilayers was found already by Meijer, Leermakers, and Lyklema (Meijer et al., 1995). The relative strength of this attraction depends on the solvent conditions and details of the phospholipid type. It is an entropic effect caused by alteration of the head-group conformations when the two bilayers come in close contact. Compellingly, the addition of even minimal amounts of PEGylated lipid on the interactions between DOPC CSLBs is perceptible (Figure 1B). Upon the inclusion of 0.5 mol% DSPE-PEG₂₀₀₀ the attractive well is seen to dissipate, with the system displaying increasingly repulsive interactions at greater PEGylated lipid concentration. Furthermore, the minimum distance between the CSLBs can be seen to significantly increase upon increasing DSPE-PEG₂₀₀₀ addition, suggesting that steric repulsion is induced by the PEGylated lipid. Based on these computations, we select CSLBs with 0, 5 and 10 mol% stabilizer for confocal imaging so as to examine experimentally the stability of and interactions between CSLBs predicted to be aggregation-prone (without stabilizer) and colloidally stable (with modest amounts, 5 and 10 mol%, of DSPE-PEG₂₀₀₀).

To determine whether the PEG chains are in the mushroom or brush regime we estimate the reduced PEG anchor density Σ from Σ = πσR _g ², with σ the anchor density and R _g the radius of gyration of a PEG chain. Using literature values for the area per lipid in the bilayer, A _L (Pyrkova et al., 2011), and the radius of gyration of PEG ₂₀₀₀, R _g = 1.8 nm (Devanand and Selser, 1991), we compute reduced anchor densities just below (Σ_{DOPC, 5 mol%} = 0.7; Σ_{DPPC, 5 mol%} = 0.8) and just above (Σ_{DOPC, 5 mol%} = 1.4; Σ_{DPPC, 5 mol%} = 1.7) for 5 and 10 mol% DSPE-PEG₂₀₀₀ in a DOPC and DPPC membrane. The small difference between the two bilayers pertains to the slightly smaller area per lipid (and thus higher anchor density, σ = A _L ⁻¹) for DPPC (A _DPPC = 0.614) compared to DOPC (A _DOPC = 0.717). This suggests that the PEG chain density is in the intermediate regime between the characteristic “mushroom” limit (Σ << 1) and “brush” limit (Σ >> 1). This is in line with the shape of by SCFT computed PEG volume fraction profiles reported previously (Giakoumatos et al., 2022), which do not exhibit a clear peak as is characteristic for grafted chains deep in the mushroom regime. It is noted that a brush layer is not essential to provide significant steric repulsion. Stenkamp and Berg showed a small amount of sufficiently long anchored chains suffices to provide enough steric repulsion (Stenkamp and Berg, 1997).

To examine the CSLB interaction as a function of membrane fluidity, by comparing fluid and gel phospholipids, and as a function of the amount of bilayer-inserted PEGylated-lipids, confocal imaging was performed at multiple particle concentrations. The cluster analysis and pair interactions of the large confocal images were computed using a Matlab script relying on circle matching, segmentation and cluster assignment based on connectivity (ESI—Supplementary Section S6). The accuracy of this method to determine cluster sizes and strength of pair interactions was confirmed using a scanning electron microscopy (SEM) image of the 3 µm silica spheres used to form the CSLBs (ESI—Supplementary Figure S7). Further, it was found that the resulting g(r) did not significantly depend on the value of r _max chosen, and so for this study r _max of 100 was fixed at 100 µm (ESI—Supplementary Section S8). As the measurements were completed in quasi-2D due to the tendency for the particles to sediment on the coverslip, here we report the concentration of CSLBs in terms of area fraction φ (ESI—Supplementary Section S5). The concentration of a colloidal dispersion is an important parameter in considering the system stability and potential for application and has a profound impact on the effective g(r). Therefore, it is important to study the impact of many body interactions in addition to the pair interaction. To thoroughly examine this, a wide range of area fractions were tested varying from dilute to concentrated (ESI—Supplementary Figure S4). Importantly, the resulting g(r) are only comparable between those samples of equivalent area fractions. For the purposes of this paper, we focus on the results of samples of relatively low (φ = 0.017) and relatively high (φ = 0.11) area fractions.

We examine the stability of and interactions between CSLBs composed of the gel phospholipid 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) or the fluid phospholipid DOPC, and the impact of imbedding PEGylated lipid in the bilayer. Specifically, we focus on CSLBs containing 0, 5 and 10 mol% of membrane anchored DSPE-PEG₂₀₀₀. The mobility of the bilayer on the silica scaffold at each of these conditions was investigated previously using fluorescence recovery after photobleaching (FRAP) (Giakoumatos et al., 2022). It was found that the membrane of DOPC and DOPC+5%DSPE-PEG₂₀₀₀ CSLBs demonstrated high fluidity, while DOPC+10%DSPE-PEG₂₀₀₀ did not recover within 10 min. This is hypothesised to be due to stiffening of the bilayer [or changes in its spontaneous curvature or thermal fluctuations (Tribet and Vial, 2008)] induced by increased amounts of the high T _m phospholipid DSPE-PEG₂₀₀₀ in the membrane, or the pinning of PEG to the silica scaffold surface impeding lateral movement. CSLBs consisting of DPPC as the primary lipid did not show recovery regardless of PEGylated lipid concentration.

Figure 2A shows confocal microscopy images of DOPC and DPPC CSLBs with 0, 5 and 10%DSPE-PEG₂₀₀₀ at high area fraction φ = 0.11. For clarity, the confocal microscopy images displayed in Figure 2A are a representative segment of the larger tilescan images analysed. It is apparent that clustering is significantly reduced when comparing confocal images of CSLBs with 0%–10% PEGylated lipid. This is most clear for the DPPC CSLBs, however, the precise configuration of particle clusters and quantification of the impact of PEGylated lipid on CSLB interaction is not possible to determine by eye. Therefore, using the image analysis approach described in ESI—Supplementary Section S6, the cluster distributions and g(r) curves for CSLBs were determined (Figures 2B–D).

Figures 2B, C show that at low CSLB area fractions the addition of PEGylated lipid to the bilayer increases the number of single particles being present for both DOPC and DPPC CSLBs, indicating the effectiveness of the steric repulsion induced by the DSPE-PEG₂₀₀₀. In compositions where 0 or 10% of DSPE-PEG₂₀₀₀ are added to the bilayer, both DOPC and DPPC CSLBs show comparable singlet stability, ∼30% and ∼65%, respectively. DPPC+5%DSPE-PEG₂₀₀₀ CSLBs demonstrated the highest stability at 75% singlets. At high area fractions, again the impact of PEGylated lipid is apparent in increasing the number of single particles. The CSLBs composed of the gel lipid DPPC show systematically lower number of singlets than DOPC CSLBs, regardless of the DSPE-PEG₂₀₀₀ concentration.

In general, at all area fractions singlets are the predominant cluster size for all investigated samples. Additionally, there appears to be a continuous decrease in the percentage of particles across the cluster sizes, with the sharpest decrease seen in samples with PEGylated lipid in the membrane (Figures 2B, C). DPPC and DOPC CSLBs without PEGylated lipid demonstrated a more gradual decrease as they tended to be more clustered already at low area fractions.

Comparing the g(r) characteristics of DOPC and DPPC CSLBs, with and without PEGylated lipids, allows for quantitative evaluation of how the type and phase state (fluid or gel like) of the main phospholipid affect the interaction strength in the colloidal system (Figure 2D). Here we focus on the interactions of fluid and gel CSLBs at high area fraction φ = 0.11. For each membrane composition the first g(r) peak occurred at r = 3 μm, and as expected all g(r) curves can be seen tending to 1 for large r. DPPC CSLBs with no PEGylated lipid demonstrated consistently a higher first peak at r = 3 µm than DOPC CSLBs, indicating a stronger attraction at that proximity (Figures 2C, D). Additionally, regardless of DSPE-PEG₂₀₀₀ concentration, gel DPPC CSLBs were seen to invariably have higher first peaks, therefore stronger interactions, than the DOPC CSLBs (Figure 2D). All samples also demonstrated a second peak at r = 6, the more pronounced being the DPPC CSLBs (Figure 2D, first panel). Visually this can be reconciled by comparing the confocal microscopy images in Figure 2A where dense, defined clusters are more obvious for DPPC CSLBs than for DOPC CSLBs.

Overall, from these results it appears that for both DOPC and DPPC CSLBs, membranes composed of 5%DSPE-PEG2000 show the lowest attractive interaction. Additionally, it is known that the membrane of DOPC+5%DSPE-PEG₂₀₀₀ CSLBs remains fluid, while DPPC+5%DSPE-PEG₂₀₀₀ CSLBs are gel (Giakoumatos et al., 2022) This indicates that DOPC+5%DSPE-PEG₂₀₀₀ and DPPC+5%DSPE-PEG₂₀₀₀ CSLB compositions are optimal for further studies where both colloidal stability and contrasting membrane fluidity are required.

Now that we have shown that the colloidal stability of the CSLBs can be improved by adding PEGylated lipids to the membrane to induce steric repulsion, it is interesting to test the boundaries of this colloidal stability. Furthermore, to consider if CSLBs could be suitable in applications such as sensing, wherein more complex media such as serum may be unavoidable, it is important to check how robust the stability of the system is in the presence of free (macro)molecules. To this end, we supplement our CSLB dispersion with a non-adsorbing polymer, 100 kDa PEG, by which we induce an attractive depletion interaction (de Hoog et al., 2001; Lu et al., 2008; Lekkerkerker and Tuinier, 2011a).

First we apply SCFT computations to elucidate the way in which the PEG depletant interacts with the CSLBs: by depletion from the bilayer or by penetration close to the silica surface (Figure 3, ESI—Supplementary Section S1). For bare silica particles, the depletant PEG can closely approach the particle surface, but it forms a depletion zone due to entropy loss (Figure 3A).

For DOPC CSLBs and DOPC + DSPE-PEG₂₀₀₀ CSLBs, the segment concentration profile of the PEG depletant shifts away from the particle surface by approximately 5 nm, which corresponds to the thickness of the lipid bilayer (Figures 3B, C) (Gumí-Audenis et al., 2015; Gumí-Audenis et al., 2016). Furthermore, the impact of depletion forces on the strength of the interactions between CSLBs was computed by SCFT for depletant concentrations ranging from 0 to 2.5c*, where c* determines the critical overlap concentration (Figure 4, ESI—Supplementary Section S11).

SCFT elucidates a strong trend of increasing attraction mediated by non-adsorbing PEG chains between both DOPC and DPPC CSLBs upon addition of depletant, regardless of membrane stabiliser DSPE-PEG₂₀₀₀ inclusion (Figures 4A, B). This indicates that the interactions between CSLBs can be tuned by multiple handles, specifically here by including stabiliser and by introducing depletion forces. Note that a (modest) repulsive contribution to the interaction between the CSLBs is found around an interparticle distance of 30 nm (Figure 4A) for the highest free PEG concentration added [ESI (Mao et al., 1995; Semenov and Shvets, 2015)] However, the attraction at shorter interparticle distances still overwhelms this weak repulsion.

By varying the amount of free polymer, the effective range and strength of the attraction between colloids can be modified.¹⁵ The polymer overlap concentration (c*) quantifies the point at which a polymer solution moves from the dilute regime, where single polymer chains do not interact with one another, to the semi-dilute or entanglement regime (ESI—Supplementary Section S11). Additionally, c*gives the concentration beyond which the addition of extra polymer will start to have a less significant effect on the strength of depletion.³⁰ For this study, we select concentrations corresponding to 0.05c* being 0.575 mg/mL. It is expected that the addition of depletant to the CSLB dispersion at the concentrations chosen would exacerbate the occurrence of dense, defined CSLB clusters, such as those seen for DPPC CSLBs at high area fractions (Lekkerkerker and Tuinier, 2011b).

Figure 5 displays the results of confocal imaging and subsequent data analysis for DPPC and DPPC+5%DSPE-PEG₂₀₀₀ CSLBs at a fixed PEG depletant concentration 0.05c ^* . These dispersions were selected as illustrative cases for systems with high and low interaction strength, respectively. The effect of steric stabilisation by DSPE-PEG₂₀₀₀ as well as the impact of the additional attraction due to the polymer depletant 100 kDa PEG on the colloidal stability of the CSLBs are clearly visible (Figure 5A).

DPPC CSLBs without stabilizer assemble into numerous dense clusters of a ramified, elongated shape and generate a space filling network (Figure 5A. Top left). This is indicative of a significant attraction between the CSLBs, which leads to fractal aggregation until the aggregates touch (de Hoog et al., 2001; Anderson and Lekkerkerker, 2002). Upon the addition of depletant, this elongated shape is even more pronounced. Larger and more well-defined clusters appear indicating gelation by arrested spinodal phase separation (Figure 5A, bottom left) (de Hoog et al., 2001; Lu et al., 2008).

By contrast, the DPPC CSLBs with 5%DSPE-PEG₂₀₀₀ stabilizer are well distributed (Figure 5A top right). Small clusters and single particles are predominant. The addition of depletant destabilizes the dispersion, which now also contains larger clusters (Figure 5A bottom-right). A noticeable number of singlets and small aggregates remains. The larger clusters appear somewhat smaller and less heterogeneous in dimensions and shape than those observed for DPPC CSLBs with (out) depletant. Presumably, the aggregates are able to reorganise, possibly as a consequence of the additional steric stabilization afforded by the PEGylated lipid. We suspect that the larger clusters accumulate at the expense of the small clusters or single CSLBs, such as by nucleation and growth (de Hoog et al., 2001). A future time-resolved imaging study could test our conjecture and reveal whether both dispersions are indeed at 0.05c* depletant in a two-phase regime of the state diagram, wherein the larger aggregates form via spinodal decomposition or via nucleation and growth, as hypothesized for the DPPC CSLBs without stabilizer and the DPPC CSLBs with 5% DSPE-PEG₂₀₀₀ stabilizer, respectively.

Interestingly, the cluster distributions (calculated for clusters up to 50 CSLBs per cluster) reveal a predominance of clusters in all systems (Figures 5B, C). More than 97% of all particles reside in clusters composed of 50 CSLBs or smaller. The clusters are smallest in the most stable dispersion (DPPC+5%DSPE-PEG₂₀₀₀ CSLBs) without depletant, wherein 100% of the particles reside in clusters composed of less than 20 CSLBs. Regardless of the presence of the stabilizer, more particles end up in larger aggregates under the influence of added depletant (Figure 6). For example, without depletion, no clusters larger than 19 particles are detected in suspensions of DPPC+5%DSPE-PEG₂₀₀₀ CSLBs, whilst under the influence of depletion, more than 10% of CSLBs are found in clusters of 20 particles or larger.

Next, the strength of attraction between the CSLBs under the influence of depletion was evaluated via analysis of the radial distribution functions (Figures 5D, E). The addition of depletant results in an increase in the height of the first two peaks and a narrowing of the second peak for CSLBs with and without stabilizer. Additional peaks at r = 9 (and in some cases 12 µm) are also more pronounced in the presence of the depletant than in its absence. All of these observations underline a substantial increase in attraction between the CSLBs upon addition of depletant, as predicted by SCFT. As expected, the strongest attraction occurs between DPPC CSLBs under the influence of depletant. The next predominant attraction occurs in DPPC+5%DSPE-PEG₂₀₀₀ CSLBs with depletant, closely followed by DPPC CSLBs without depletant. CSLBs of DPPC+5%DSPE-PEG₂₀₀₀ CSLBs without depletant are least attractive. These results unambiguously demonstrate that the attraction between CSLBs can be modulated by PEGylation and/or addition of depletants. Not only is it possible to induce stability and reduce attraction between DPPC CSLBs by incorporation of a PEGylated lipid into the bilayer, but it is also possible to strengthen the attraction via depletion.