Nanoparticle-Lipid Interaction : Job Scattering Plots to Differentiate Vesicle Aggregation from Supported Lipid Bilayer Formation

The impact of nanomaterials on lung fluids or on the plasma membrane of living cells has prompted researchers to examine the interactions between nanoparticles and lipid vesicles. Recent studies have shown that nanoparticle-lipid interaction leads to a broad range of structures including supported lipid bilayers (SLB), particles adsorbed at the surface or internalized inside vesicles, and mixed aggregates. Today, there is a need to have simple protocols that can readily assess the nature of structures obtained from particles and vesicles. Here we apply the method of continuous variation for measuring Job scattering plots and provide analytical expressions for the scattering intensity in various scenarios. The result that emerges from the comparison between modeling and experimental measurements is that electrostatics plays a key role in the association, but it is not sufficient to induce the formation of supported lipid bilayers.


I -Introduction
The emission of fine and ultrafine particulate matter in the environment is responsible for the increase of mortality and morbidity from cardiorespiratory diseases worldwide [1][2]. In the context of environmental pollution, engineered nanoparticles which sizes are less than 100 nm have attracted much attention and been identified as potentially harmful. When inhaled, these particles are able to reach the respiratory zone in the lungs and enter in contact with the alcinar region composed of hundreds of millions of alveoli [3][4]. Several scenarios of nanoparticles passing from the alveolar spaces towards the blood circulation have been examined recently and in some case studies the crossing of the air-blood barrier has been demonstrated [4]. It is found that in the alveolar spaces, the nanoparticles first come into contact with the pulmonary surfactant, a fluid composed of lipids (90%) and proteins (10%) which provides important functions in the lung physiology [5][6]. This scenario prompted researchers to actively study the interactions between nanoparticles and lipid vesicles, typically with vesicular structures in the size range 100 nm to 1 μm [7][8][9][10].
Another example where particles interact directly with biological membranes is the process of endocytosis [11]. Endocytosis is the biological process by which nano-objects of different nature and sizes, including pathogens, bacteria, virus, nanoparticles etc… are internalized inside living cells. For particles larger than 1 µm, the process is referred to micropinocytosis, whereas for 100 nm nanoparticles the passage through the membrane can be passive or active, this later being mediated by caveolin or clathrin proteins [12]. When nanoparticles are close to a cell membrane, the interactions generate forces of different origins (e.g. van der Waals, electrostatic), leading to the membrane wrapping around the particles and cellular uptake [13][14][15].
Strategies based on the use of more biological models and substitutes have been also proposed [17,[27][28][29]]. Depending on the particle size, charge and hydrophobicity, several mechanisms have been suggested, leading to a wide variety of hybrid structures. Fig. 1 displays a library of nanoparticle-membrane structures observed using cryogenic transmission electron microscopy (cryo-TEM). They include nanoparticles coated with a single bilayer (called nano-SLB in the following, Fig. 1a) [17,28], particles embedded with the lipid membrane or adsorbed at the surface ( Fig. 1b and 1c respectively) [30][31], particles internalized inside the lipid compartment ( Fig. 1d) [32] and mixed nanoparticle-vesicle aggregates (Fig. 1e) [18]. In the case of particle internalization, the fluid membrane invaginates and envelops one or several particles like in cellular endocytosis [11]. Despite many efforts, the mechanisms of particles interacting with the synthetic or biological membranes are not fully understood.
A broad range of experiments was used to study particle-membrane interaction. These experiments include, among others light scattering [17,33], leakage assays [18], quartz crystal microbalance [34], electron and fluorescence microscopy [17,[24][25][30][31][32]. Cryogenic transmission electron microscopy is probably one of the best methods to visualize the nanoparticle-membrane structures, as illustrated in Fig. 1 [35]. It has the required resolution (~ 1 nm) and electronic contrast to identify both nanoparticles and lipid membranes. Cryo-TEM images however lack of statistics, as only a few objects are usually displayed. In this context, there is need to develop simple protocols that can rapidly assess the nature of structures obtained from particles and vesicles. Here we provide examples of light scattering based analytical models that are able to discriminate among the different association scenarios illustrated in Fig. 1. The approach is developed for static light scattering but could be extended as well to small-angle neutron and X-ray scattering or UV-visible spectroscopy. To this aim, we use the method of continuous variation developed by Paul Job, leading to what we describe as Job scattering plots [36][37][38][39][40][41]. Here we provide analytical expressions for the Rayleigh ratio obtained from mixed nanoparticle-vesicle aggregates and particle coated with a single bilayer, respectively. Quantitative comparisons with experimental data are also discussed.  [17]; b) Gold particles embedded within the lipid membrane of a vesicle [31]; c) Silica particles adsorbed at the surface of a vesicles [30]. d) Silica particles internalized inside the lipid compartment [32]. e) Aggregates of ZnO nanoparticles and vesicles [18]. The upper panels provide an illustration for the different structures.

II -Experimental
Nanoparticles: Aluminum oxide nanoparticles from Disperal® (SASOL, Germany) have the shape of irregular platelets of sizes 40 nm in length and 10 nm in thickness [33]. To obtain homogeneous dispersions, the alumina powder is dissolved in a nitric acid solution (0.4 wt. % in deionized water) at the concentration of 10 g L -1 and sonicated for an hour. The particles have an hydrodynamic diameter = 64 nm. The positively charged silica particles were synthetized using the Stöber synthesis. Following the synthesis, the silica were functionalized by amine groups, resulting in a positive coating [17,23,42]. Aminated silica were synthesized at 40 g L -1 and diluted with DI-water at pH 5. The hydrodynamic and geometric diameters were determined at = 60 nm and = 41.2 nm. Negative silica particles (trade name CLX®) were purchased from Sigma Aldrich at the concentration of 450 g L -1 . The batch was diluted down to 50 g L -1 and dialyzed against DI-water at pH 9 for two days. The diameters were measured at = 34 nm and = 20 nm [23]. The particle surface charge densities were determined using the polyelectrolyte assisted charge titration spectrometry [39], leading densities of +7.3e, +0.62e and -0.31e nm -2 respectively. In the following, the particles are abbreviated Alumina (+), Silica (+) and Silica (-).

III.1 -Job scattering plots
In 1928, Paul Job developed the method of continuous variation to determine the stoichiometry of binding (macro)molecular species in solutions, providing information about the equilibrium complexes. We have adapted this technique to study interactions in soft condensed matter using small-angle scattering techniques. In the cases of coacervation or microphase separation , the Job scattering technique allows to screen large domains of phase diagrams and to detect phase boundaries [43]. In the cases of protein forming corona, of polymer or lipid adsorption on nanoparticles, the method is quantitative and provide some key features of the association, e.g. the stoichiometry, the layer thickness and density [41,44]. In this work, emphasis is put on static light scattering and the modeling of attractive interaction between nanoparticles and lipids. This approach leads to analytical expressions for the scattering intensity during aggregate or SLB formation.
More specifically, we are concerned with ternary phase diagrams for which the total active concentration = + is constant and the ratio between the two concentrations is varying continuously according to = ⁄ , where and are the nanoparticle and vesicle concentrations, respectively. In practice, is held in the range 0.01 -10 g L -1 and = 10 -3 -10 3 .
This technique has several advantages, one of them being that the solutions are in the dilute regime and that the Debye-Gans theory applies to all solutions [45]. The approach also relies on the fact that the scattering intensity arising from different species is additive, leading to: where the index refers to the different types of scatterer. In this work, 4 types of scatterers are considered: engineered nanoparticles, lipid vesicles, hybrid aggregates and supported lipid bilayers. In Eq. 1, is the scattering contrast coefficient, the weight-averaged molecular weight, , the radius of gyration and 2, is the second virial coefficient. In the following, the form factor (1 − 2 2 /3) and the interaction contribution 2 2 will be neglected for sake of simplicity, leading for the Rayleigh ratio an expression of the form: The scattering intensity arising from nanoparticle and vesicle mixed solutions is now provided for three basic behaviors, the case of non-interacting species, the aggregate formation (Fig. 1e) and the nano-SLB (Fig. 1a).

III.2 -Nanoparticle-vesicle hybrid aggregates
Here we consider that the particle-vesicle interaction is attractive and leads to the formation of mixed aggregates. The model is general and does not specify the interaction type. As the scattering varies linearly with the weight-averaged molecular weight of the scatterers, the presence of aggregates will lead to an excess scattering compared to the non-interacting case (Eq. 3). For sake of simplicity, it is assumed that ( , )-aggregates are formed and composed of nanoparticles and vesicles. The aggregate molecular weight thus reads = + . This later equation has an important consequence, namely that at the critical stoichiometric ratio , all the particles and vesicles put in the solution will be in aggregates, leading to the relationships: The above results also suggest that the overall mixing diagram can be decomposed in two regions: Eq. 3. Note that these calculations could be easily extended to other types of assemblies such as particles embedded in the membrane, vesicles decorated with nanoparticles or particles internalized inside the membrane compartment. In these latter cases, the molecular weight and the stoichiometry should be adjusted to take into account the modeled structure. For nano-SLB, there also exists a critical mixing ratio for which all the particles are covered with a single lipid bilayer and form a supported lipid bilayer (Fig. 1a). At , the nanoparticle and vesicle surface area concentrations are equal, so : where and denote the specific surface areas for nanoparticles and vesicles respectively.

III.4 -Comparison with experiments
In this part we study the interactions between nanoparticles and vesicles and compare Job scattering plots obtained experimentally with the above predictions. For the experimental studies,

IV -Conclusion
In this work we study the interaction of engineering nanoparticles with lipid vesicles and search for prominent features pertaining to their scattering properties. The first goal is to provide tools to characterize the different types of structures resulting from synthetic/biological membranes and nanomaterials, an issue that is relevant in many biophysical applications. The second objective consists in writing down quantitative predictions for the scattering of dilute solutions, allowing to differentiate between the formation of aggregates and that of supported lipid bilayer. The expressions for the scattering cross-sections are simple and analytical, and they show the relevance of the Job scattering plot approach, as different association scenarios can be discriminated. It is found for instance that the SLB formation is associated with a decrease of the scattering intensity, whereas the aggregate formation is associated with an increase in light scattering. The models proposed are also implementable as the form factor, the dispersity or the interaction of the particles and vesicles can be taken into account into the equations. The result that emerges from the experiments on alumina and silica particles is that electrostatics plays an important role in the association, but is not sufficient to induce the formation of supported lipid bilayers.