Use of nanoparticle concentration as a tool to understand the structural properties of colloids

Elucidation of the structural properties of colloids is paramount for a successful formulation. However, the intrinsic dynamism of colloidal systems makes their characterization a difficult task and, in particular, there is a lack of physicochemical techniques that can be correlated to their biological performance. Nanoparticle tracking analysis (NTA) allows measurements of size distribution and nanoparticle concentration in real time. Its analysis over time also enables the early detection of physical instability in the systems not assessed by subtle changes in size distribution. Nanoparticle concentration is a parameter with the potential to bridge the gap between in vitro characterization and biological performance of colloids, and therefore should be monitored in stability studies of formulations. To demonstrate this, we have followed two systems: extruded liposomes exposed to increasing CHCl3 concentrations, and solid lipid nanoparticles prepared with decreasing amounts of poloxamer 188. NTA and dynamic light scattering (DLS) were used to monitor changes in nanoparticle number and size, and to estimate the number of lipid components per particle. The results revealed a strong negative correlation between particle size (determined by DLS) and concentration (assessed by NTA) in diluted samples, which should be adopted to monitor nanocolloidal stability, especially in drug delivery.

in the literature, probably due to the indispensable operator training for the so-called 'visual validation' of NTA determination 8 . Until 2011, only two works had employed the number of nanoparticles as a parameter to evaluate nanotoxicity in ecotoxicity/environmental studies, against 18 others that compared DLS and NTA in the characterization of particle size and distribution 9 .
In 2016, when NTA was 10 years old, the International Standard Particle Tracking Analysis Guide (ISO 19430) was launched, providing specifications for the measurement of particle size distribution and concentration in nanosystem characterization using NTA. The guide preconizes the use of number-based particle size distribution and direct results interpretation, and specifies quality technical parameters, among others 16 . Nanoparticle concentration seems to be the bridge over the current abyss between in vitro characterization data and in vivo performance of nanosystems.
In this study, we firstly compared DLS (standard) and NTA (novel) in the evaluation of particle size and polydispersity of extruded liposomes composed of hydrogenated soy phosphatidylcholine: cholesterol (HSPC:Chol, 2: 1 mol%). The accuracy of the NTA method for laboratorial formulations was confirmed for this (two lipid) heterogeneous formulation. Then, taking into account that size distribution is a good indicator of instability for colloidal systems, we checked whether changes in this parameter would directly affect the number of nanoparticles in the system. For that, we intentionally destabilized unilamellar liposomes (composed of dipalmitoyl phosphatidylcholine, DPPC) and solid lipid nanoparticles (SLN, composed of cetyl palmitate and poloxamer 188) to evaluate the correlation between particle size (measured by DLS) and nanoparticle concentration (NTA). In this context, we show here the advantages of using NTA to investigate the stability of colloidal systems, focusing on those designed for the delivery of active molecules (drug delivery systems).
Destabilization of nanostructured colloidal systems. Two different colloidal systems were prepared, and their dispersed nanoparticles were destabilized to form larger ones. Transmission electron microscopy (TEM) was carried out to characterize the great morphological changes in the colloidal systems after destabilization. During the destabilization process, particle size and concentration (assessed by DLS and NTA, respectively) were followed, and the correlation coefficient (r) between them was registered.
DPPC liposomes. First, liposomes composed of DPPC (0.125 mM) were extruded six times through 100 nm polycarbonate membranes. The resulting unilamellar vesicles were then destabilized with increasing chloroform (CHCl 3 ) concentrations. The addition of small aliquots of CHCl 3 to the extruded liposomes increased the particle size measured by DLS, from 116 ± 1.8 nm (CHCl 3 -free) to 658 ± 17 nm ( Fig. 2A), in the presence of CHCl 3 (2: 100 v/v).
Solid lipid nanoparticles. Five SLN formulations with the same lipid concentration (cetyl palmitate, CP = 10%) and decreasing concentrations of the non-ionic surfactant poloxamer 188 (PL = 5% to 0.1%) were prepared and analysed by DLS, NTA (Fig. 3A), and TEM ( Fig. 3C-F). A reduction in PL concentration induced changes in particle size -which ranged from 232 to 1644 nm -accompanied by a decrease in nanoparticle concentration -from 6.0 × 10 13 to 0.4 × 10 13 particles/mL. The inverse correlation between particle size (DLS) and nanoparticle concentration (NTA) was detected (r = −0.81, Fig. 3B). Accordingly, the number of CP molecules per SLN increased from 2.0 × 10 6 to 2.6 × 10 7 , as shown in Table 2. The variation in particle size observed for SLN1 and SLN5 was also demonstrated by TEM ( Fig. 3C-E). However, quantification of the particle size distribution using ImageJ software was only possible for SLN1 ( Fig. 3F) since the polydispersity of SLN5 curbed its micrographic analysis.

Discussion
A considerable number of studies have compared the DLS and NTA methods, showing the accuracy, advantages and drawbacks of each technique, and considering their peculiarities. However, all those studies have employed standard nanoparticles, such as polystyrene beads 8,17,18 . Such ideal systems do not reproduce the size distribution of formulations developed in research laboratories, which have a less homogeneous size distribution. Hence, to compare the DLS and NTA methods, we prepared different and more realistic lipid-based colloidal systems: liposomes and SLN.  DLS is the gold standard method for characterizing colloidal systems, despite its poor accuracy for highly polydisperse samples and non-spherical particles 8 . This explains the differences in particle size of liposomes with 0 or 1 extrusion passages, measured by DLS and NTA. The particle-by-particle counting approach adopted by the NTA method provides robust characterization of heterogeneous particle size distribution, since -differently to DLS -changes in the intensity of light scattered by large and small particles do not affect determination of the hydrodynamic diameter by NTA 9 . This is particularly useful for the characterization of a colloidal system formed by a complex mixture of submicron and nanometric particles 17 , such as biomimetic systems (liposomes) and membrane fractions (e.g. exosomes, buddings, detergent-resistant membranes) 7 .
Size vs. number of particles during extrusion of liposomes. As expected, the particle size, PDI, and Span values of liposomes decreased as a function of the number of extrusion cycles, measured by both methods. At the end of the extrusion cycle, the liposome diameters determined by these two techniques were very similar and strongly positively correlated. Accordingly, the PDI (DLS) and Span (NTA) values were lower than 0.2 and 1, respectively, characterizing a monodisperse distribution 19,20 . Both techniques were analytical for characterization, but NTA has the advantage of using highly diluted samples (ca. 200 times higher than DLS). These results demonstrated the accuracy of NTA in the determination of particle size and nanoparticle concentration in colloidal systems.
Changes in liposome concentration (particles/mL) during the extrusion cycle were also monitored ( Fig. 1A) with NTA. As expected, the extrusion process led to a higher number of small particles originated from the larger multilamellar ones 21 . From non-extruded liposomes to liposomes submitted to the complete (6) extrusion cycle, a directly proportional increase in the number of nanoparticles was registered. Yet the decrease in vesicle size was accompanied by enhancement in the number of liposome particles in suspension, suggesting that these parameters are related and should be explored in more depth.
Estimation of the number of lipid molecules per liposome particle. During extrusion, the number of lipid molecules per liposome decreased, as exemplified for HSPC molecules (Fig. 1A). The number of HSPC/ liposome, as shown in Table 1, was taken directly from the number of lipid molecules in the 0.125 mM liposomal suspension (7.5 × 10 16 ) divided by the number of particles determined by NTA. Using an alternative method, as shown in Fig. 4A, we estimated the number of lipid molecules that could be loaded per liposome of a given size, and the values agree very well with those determined from NTA data. To estimate the number of lipids/vesicle, we    first calculated the surface (sphere) area of the liposomes from their average sizes (measured during the extrusion process, either by DLS or NTA). Twice the surface area (equivalent to the internal and external monolayers of the liposomes) was then divided by the area occupied by each phosphatidylcholine molecule (55 Å 2 ) 22 to give the number of lipids/vesicle. Also, by dividing the number of lipid molecules in the 0.125 mM liposomal suspension (7.5 × 10 16 ) by the theoretical number of lipids/vesicle (estimated as indicated above - Fig. 4A), we could predict the number of particles/mL -according to DLS and NTA average size -as shown in Fig. 4B. As the extrusion process proceeds towards a monodisperse system, the predicted and determined numbers become closer and closer, converging at 2 × 10 11 particles/mL. Once more, the good agreement found between the calculated nanoparticle concentration and that determined by NTA confirms the certainty and applicability of this technique.
Destabilization of nanostructured colloidal systems. The most common events affecting the physicochemical stability of nanostructured colloids are coalescence, agglutination, and the Ostwald ripening. These processes result in larger and heterogeneous-sized nanoparticles 1 , preventing their application. In an attempt to mimic such processes, two different colloidal systems were prepared, and their dispersed nanoparticles were destabilized to form larger ones.
Liposomes composed of DPPC (0.125 mM) were destabilized upon addition of chloroform (CHCl 3 ). The destabilizing effect of CHCl 3 on lipid bilayers occurs by partial solubilization of the lipid's acyl chains 23 , and has been broadly explored over decades 24 . The addition of CHCl 3 aliquots provided a relevant increase of particle size, measured by DLS and confirmed by TEM. The absolute size measured by TEM differed to that measured by DLS because of the well-known limitations of this technique, such as shrinkage and deformation of nanoparticles during the drying process 25 in sample preparation. Nevertheless, the micrographics confirmed the formation of larger liposomes following the CHCl 3 treatment. Inversely, and as expected, the nanoparticle concentration decreased with increased CHCl 3 concentration, confirming liposome destabilization.
In another set of experiments, a binary, and therefore more complex, lipid-based system of SLN was prepared. Five formulations with the same concentration of lipid (CP = 10%) and different amounts of the non-ionic surfactant PL (5 to 0.1%) were prepared. PL is known to stabilize lipid nanoparticles, physically preventing their agglutination 26 . Thus, at low PL concentrations, SLN stability was not maintained, contributing to nanoparticle aggregation (which prevented quantitative analysis by TEM). As expected, a lack of PL was accompanied by a drastic increase in particle size and number of lipids/particle, and by a decrease in nanoparticle concentration in SLN formulations (Fig. 3 and Table 2).
Altogether, destabilization of the nanostructured colloidal formulations was confirmed by all methods evaluated. The effects of destabilization were similar in both the liposome and SLN systems: an increase/decrease in nanoparticle size and concentration, respectively. The correlation coefficients between these parameters were determined for liposomes (r = −0.92, Fig. 2) and SLN (r = −0.81, Fig. 3). The correlation was higher for liposomes than SLN, probably due to the complex structural molecular organization of the latter. Considering the potential application of nanoparticle concentration in in vitro characterization and biological and clinical studies, such achievements indicate that particle size and concentration are strictly (inversed) related in different pharmaceutical colloidal systems, and should be used to monitor the physicochemical stability of formulations.
It is worth mentioning that monitoring of nanoparticle concentration over time can also help early detection of system instability, such as in the case of nanoparticle degradation, evidenced by a decrease in the number of particles without a concomitant increase in nanoparticle size. So far, only a few studies have adopted evaluation of nanoparticle concentration in the physicochemical stability analysis of pharmaceutical 4,27,28 and environmental 13 formulations.
The number of nanoparticles can be expressed as the molar concentration of colloidal particles in the formulation 11 , and this allows the estimation of the number of excipient molecules that compose each individual particle 4 , two important parameters that represent a real advance in the structural elucidation of nanocolloids.
We have shown here, for a single component formulation (DPPC liposomes), that the number of lipid molecules per vesicle can be determined from the nanoparticle concentration data, considering the number of lipid molecules in suspension (Table 1). Following the addition of solvent, the resulting destabilized liposomes (of greater size and lower concentration) showed increasing numbers of DPPC molecules per nanoparticle, in comparison to the initial (stable) vesicles. Similar results were observed with SLN (Table 2), for which destabilization was caused by low ratios of surfactant.
Taking into account the importance of nanoparticle concentration in determining the biological effects of colloidal systems, we foresee that there should be an ideal range for the number of nanoparticles in suspension, and we will endeavour to identify the acceptable limits of nanoparticle concentration. In this study we have shown that NTA is a simple, cost-effective, and real-time method for evaluating nanoparticle concentration. Therefore, it is essential to include this parameter in physicochemical stability studies of nanostructured colloidal systems intended for multipurpose applications, as well as to guarantee the quality of nanocolloidal products.

Conclusions
The simple premise that significant changes in particle size and distribution indicate instability of a colloidal system formed the basis of our hypothesis. We have shown relevant evidence to support the idea that the concentration of nanoparticles measured by NTA should be a parameter followed in determining the physicochemical stability of colloids. The strong negative correlation between particle size assessed by DLS and nanoparticle concentration demonstrated that both parameters serve to monitor colloidal instability. In addition, in the case of nanoparticle instability (erosion, disruption or degradation), which directly affects colloidal system performance, the phenomenon can be prematurely predicted by monitoring the nanoparticle concentration, a measure that is not currently adopted in physicochemical stability studies. This is especially relevant due to increasing interest in this parameter as analytical information in biological and clinical studies. The number of colloidal particles in suspension may be the key to crossing the abyss between in vitro data and in vivo studies, reinforcing the relevance of monitoring nanoparticle concentration over time.
Colloidal system preparation. Liposomes. Two different liposomal formulations were prepared, at a final lipid concentration of 0.125 mM: i) vesicles of DPPC, which were employed in liposome destabilization tests; and ii) vesicles of mixed composition, prepared with HSPC:Chol (2: 1 mol%), which were used to evaluate the number of extrusions necessary to reach a stable formulation of monodisperse particle size distribution.
Both formulations were prepared from stock chloroform lipid solutions. After the proper volumes of lipids were pipetted, the solvent was removed under nitrogen flux to create a thin lipid film in a round-bottom flask. The film was left to dry in a vacuum for 2 h to ensure the removal of any solvent trace. After that, the thin lipid film was hydrated with deionized water and vortexed (5 min) to form multilamellar liposomes.
DPPC multilamellar vesicles were extruded six consecutive times through polycarbonate membranes (100 nm pores) in order to obtain unilamellar vesicles of homogeneous size distribution 29 ; the particle size and concentration of the final formulation were measured by DLS and NTA, respectively.
HSPC:Chol multilamellar liposomes were also extruded six times through the (100 nm pore) polycarbonate membranes, but after each extrusion, the size distribution and nanoparticle concentration were evaluated by DLS and NTA.
Solid lipid nanoparticles. SLN were prepared by the emulsification-ultrasonication method 30 . Specifically, the solid lipid (10% CP) was heated to 10 °C above its melting point, under magnetic stirring. The aqueous phase was prepared with appropriate amounts of PL in water, and heated to the same temperature as the lipid phase (64 °C). This phase was then dropped into the oily phase, under high-speed agitation (10,000 rpm) using a Turrax blender (IKA Werke Staufen, Germany) for 2 min. The obtained microemulsion was sonicated (Vibra-Cell, Sonics & Materials Inc., Danbury, USA) at 500 W and 20 kHz, in alternate 30 s cycles (on and off) for 15 min, and immediately cooled to 25 °C.
Induced destabilization of colloidal systems. DPPC liposomes. DPPC liposomes were used to evaluate size distribution and nanoparticle concentration during destabilization induced by solvent. Briefly, small aliquots of chloroform were added to 1 mL of the liposome suspension to a final ratio of 0.5: 100, 1: 100, 1.5: 100 or 2: 100 (v/v), and the sealed vials were stirred for 30 s on a vortex. After 1 h, destabilization was monitored through DLS (particle size) and NTA (nanoparticle concentration) measurements.
Colloidal system characterization. Dynamic light scattering. Particle size and polydispersity index (PDI) of liposomes and SLN were analysed via laser light scattering (DLS) using Zetasizer Nano ZS90 equipment (Malvern Instruments, Worcestershire, UK). Liposomal samples were used without dilution but SLN samples were diluted 1000 times. The results are given as mean plus standard deviation (n = 3).
Nanoparticle tracking analysis. Particle size, Span, and nanoparticle concentration were assessed by NTA, carried out with a NanoSight NS300 (Malvern Instruments, Worcestershire, UK) equipped with a sample chamber and a 532 nm laser. The colloidal systems were diluted 200 times and 50,000 times, for liposomes and SLN, respectively, with around 2000 tracks counted in each measure. The colloidal systems were injected into the sample chamber with sterile syringes until the liquid extended to the tip of the syringe; measurements were performed in triplicate at room temperature.
Transmission electron microscopy. Transmission electron microscopy (TEM) images of liposomes and SLN formulations were measured in a JEOL 1200 EXII microscope, operated at 80 kV. Uranyl acetate (2%) was added to the diluted samples; after that, aliquots were dropped into copper grids coated with a carbon film, and dried at room temperature. After drying, micrographs of the formulations were taken at different magnifications. Data availability. All data generated or analysed during this study are included in this manuscript.