Labeling biomolecules and cells with organic fluorophores are representative tools for studying the underlying complex interactions and the dynamics in metabolic processes in various time and length scales. Recently, these organic fluorophores have been gradually replaced by nano-size semiconductor nanocrystals  such as quantum dots (QDs).
This preference for QDs results from several remarkable optical properties of QDs. In contrast to organic fluorophores, QDs have a higher quantum yield, and a narrower and more symmetric emission spectrum which can be controlled by tuning the core size of the QDs during synthesis procedures. Furthermore, the photo-bleaching effect of QDs is much weaker compared to organic fluorophores. However, before introduction into biological environments, the surface of QDs should be transformed to hydrophilic with the help of amphiphilic molecules or other surface-capping materials due to the hydrophobic surface property of QDs. In recent years, several groups reported passivation of QDs by phospholipid, which is a building unit of the cell membrane  - . One good example is QLC (Quantum dot-Liposome Complex) which is a giant unilamellar vesicle with QDs incorporated in the lipid bilayer    .
QLC is good candidate for biomedical imaging in site of specific drug delivery. For instance, biological fusion area between QLCs and biological targets can be fluorescent by conjugating with QDs and macromolecules such as cell membrane . In addition, if QDs coexist with organic fluorophores in the lipid bilayer of QLCs, fluorescence resonance energy transfer (FRET) signal can be observed in a nano-scale confined system of a lipid bilayer .
In spite of the various potential applications of QLCs, we still lack detailed knowledge and quantitative approaches regarding the interactions and dynamics between QDs and lipids during QLC formation. And there is still no reliable experimental data regarding the exact position of QDs in the lipid bilayer. In this work, we assume that QDs are approximated as hydrophobic hard spherical particles, and there are no specific interactions other than hydrophobic interactions. Therefore, QDs are spontaneously incorporated into the lipid bilayer of lipsomes during the self-assembly process due to strong hydrophobic interactions between QDs and phospholipids in hydrophilic environment and are positional at the center of the lipid bilayer.
In our previous work, we proposed a theoretical model by interfacial energy for a quantum dot (QD)-lipid mixed system based on a simple geometrical assumption for a single-component lipid (DOPC) monolayer deformation profile  . And we studied the stability problem of QDs inside the lipid bilayer depending on the size of QD as shown Figure 1 and experimentally proposed QLCs, which are GUVs (Giant Unilamellar Vesicles) with QDs below critical QD size loaded into the DOPC lipid bilayer. But, in our previous study, we did not observe any QLCs for the orange-emission QDs (2 - 2.15 nm) and red-emission ones (~2.5 nm) above specific QD size .
Figure 1. QD is embedded in the thin lipid bilayer depending on the size of QD. Box dotted line shows TEM image of CdSe-QD: left QD size D: 2.45 nm and right QD size D: 4.58 nm. This scale bar is about 10 (nm).
In the present work, however, we do detect a fluorescent signals from orange-emission QDs (~2 - 2.15 nm) and red-emission QDs (~2.5 nm) above critical QD size in the mixture of DOPC and DOPG. To interpret these experimental results, we propose a simple theoretical model based on geometric considerations of deformed lipid monolayer surrounding a QD in terms of the molecular packing parameter and the conformational change of the lipid chain instead of complicated elastic free energy calculations. This model explains our experimental observation of shift of the specific QD size.
2. Background and Model
According to Israelachvili’s work  , given the packing parameter P of a given lipid, the minimum radius of the special liposome is determined as follow. Figure 2 shows a uni-bilayer liposome with the in-outer layer ( ) and the outer layer thickness ( ) in a single liposome. For liposome of the outer layer volume and the outer surface area with molecules, there are following relations between them .
Here, v is the volume of simple hydrocarbon molecule. The area per head group (a) is
Figure 2. Uni-bilayer liposome and inner and outer monolayer structures.
Here, ( ) is the actual area per head group. If Equation (3) is divided by a0, the ratio of the actual area a to the optimal area a0 is given by
Here, a0 is referred to as the optimal surface area per molecule, defined at the hydrocarbon-water interface.
Equation (4) gives the area ratio as a function of the packing parameter ( ), the critical chain length ( ), the out radius ( ), and the thickness of the outer layer ( ). If the packing parameter and critical chain length are fixed, the ratio of the area to the optima head area ( ) will approaches 1 with a decrease of the out radius ( ). This condition approaches to the lower possibility for liposome formation. When the minimum value of is reached, the smallest liposome can be formed. The out radius ( ) replace the value of , we refers to . Substituting , and , expressed as a formula according to ,
From Equation (5), the minimum radius is
Here, the packing parameter is .
For truly fluid hydrocarbon chains, meanwhile, the optimal head area should not depend strongly on the chain length or on the number of chains. We can define the critical chain as the maximum effective length of the hydrocarbon chain in the liquid state. The semi-empirical definition of the hydrocarbon chain length was theoretically interpreted by Israelachvili  Tanford  and Lindman . for the saturated hydrocarbon chains is
Here, stands for the length of the fully extended hydrocarbon chain, and n is number of carbon atom for each hydrocarbon tail. However, as may be expected, is of the same order as, though somewhat less than, the fully extended molecular length of the chain . It can be seen that the minimum size of a liposome ( ) depends on the packing parameter ( ) and on the critical chain length ( ). Since v and are fixed, the only way to reduce the packing parameter ( ) is increasing the optimal head area ( ).
The key point of this model would define the critical QD radius by limiting the to cover part of the void around the QD at graph. For the definition of in this model, we considered only the size of QD core excluding ligand (hexadecylamine).
Equation (6) shows the minimum possible radius of the spherical liposome, which is composed of the lipids with the packing parameter P. We first assumed that the maximum possible curvature of the lipid monolayer with thickness d around the QD of radius r has its limit at the value to evade any unfavorable surface energy penalties. In other words, is the critical radius below which a bilayer cannot curve without introducing unfavourable packing strains such as QD inside the lipids. Therefore, when the size of each QD is smaller than , as in our experiment, the curvature of the monolayer around the QD is approximated as , and the deformed monolayer profile is a circular arc of radius as shown in Figure 4.In the case of Egg-PC lipid liposome,the packing parameter value is known to be 0.85( ; , and ) . Therefore, we know that of Egg-PC liposome can get the value of 10.8 nm from Equation (6).
We can also introduce two parameters related to the conformational variation of the hydrocarbon chain around the QD: the compressing extent h of the hydrocarbon chain and the maximum stretching extent S of the hydrocarbon chain in order to remove void formation around the QD. In the case of Egg-PC lipid, a saturated hydrocarbon chain is approximately composed of n = 18 of carbon number about 70%. When the number of carbon is n = 18, we defined form Equation (7). If S has only to contact with ligand, as shown in Figure 3(a), we can also assume that the most stretched (longest) chain is
Figure 3. (a) A model representing the deformed monolayer due to the incorporation of a QD inside the lipid bilayer (b) A plot of chain length of the most stretched lipid, Smax as a function of the QD radius, r; The dotted line corresponds to the minimum radius Rmin of deformed lipid monolayer around QD.
located in a corner of the QD direction (point B in Figure 3(a)) to remove the void formation between lipid and QD. Here, we approximately considered the distance between point B and C as ligand length (~1 nm). For the maximum extent, we can define as 3.43 nm (the ligand length plus ). And we assumed that the compression of the chain occurs at the top of the QD, as shown in Figure 3(a). In the case of maximum compression, the lipid monolayer thickness at point A is represented by from the Egg-liposome thickness due to .
The distance S from the corner of the QD to the point on the circular arc of radius for a given can be expressed as
Equation (8) is differentiated with respect to to obtain the minimum that is required to be equal to the chain length of the most stretched lipid among the lipids around the QD of radius r. Figure 3(b) shows a plot of as a function of the QD radius r. can’t exceed the maximally stretched chain length, ligand length (~1 nm) plus , which is 3.43 nm in this case . Otherwise, there would be a void formation at the ligand portion that is connected with corner of the QD. Therefore, the critical QD size is , where the chain is maximally stretched to (corresponding to the horizontal dashed line in Figure 3(b)).
In Figure 3(a), at point S, the curvature is divided by positive and negative. In the case of this model, we took only positive curvature into account. The part of negative curvature does not fully need to stretch because one of the principal curvatures is close to the monolayer spontaneous curvature of the DOPC. In other words, the regions of positive curvature require the highly curved lipids to cover the rapid increase of the area above critical, while the parts of negative curvature which have non-charged head-group can be decreasing the mechanical stress generated by a packing constraint between ligands and the head-group above critical size.
3. Experimental Methods and Materials
In this experiment, we used four different kinds of lipid molecules: L-α-phosphatidylcholine (Egg-Pc), 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC), 1,2-dioleoyl-sn-glycero-3-[phospho-rac-(1-glycerol)] (DOPG), and 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC), which were purchased from Avanti Polar Lipids. In the case of DOPC and DOPG, number of carbon atom for each hydrocarbon tail is n = 18 and DPPC is n = 16.
Before sample preparation, they were dissolved into chloroform at a determined concentration. Deionized water was obtained from a Milli-Q plus 185 (Millipore, Molsheim, France) ultra-pure water system with a resistivity of ≥18 MΩ/cm. Five different sizes of hexadecylamine (~1 nm)-coated CdSe QDs dispersed in toluene were purchased from Sigma-Aldrich. Each of them has a different core radius; blue (~1.05 nm), green (~1.25 nm), yellow (~1.65 nm), orange (2.0 - 2.15 nm) and red-emission (~2.5 nm).
3.2. Preparation of QLC
QLCs were synthesized by using the mixed solutions of QDs and phospholipids via the electroformation method  in conjunction with spin-coating technique  , as shown in Figure 4. Egg-PC (10 mg/1ml) and a mixture of DOPC lipid: DOPG lipid = 1: 1 (5 mg/1ml, molecular weight) and QD (5 mg/1ml) was prepared with the volume ratio of mixed DOPC and DOPG lipid solution:QD solution = 700 μl:25 μl. This well-mixed solution was deposited onto the ITO substrate, then spin-coated at 600 rpm for 100 s under a stream of nitrogen gas. This QD/lipid thin film was immediately dried out in a vacuum oven for 2 h to remove excess organic solvents. A home-made chamber for electroformation was built by combining two transparent conducting indium tin oxide (ITO) substrates (4 × 4 cm2, <50 Ω); one is clean and the other has a dried thin film
Figure 4. Preparation of QLCs in the order of spin-coating, drying-out QD/lipid thin film, and electro-swelling under an AC field. (a) Spin coating procedure (b) Schematic diagram of the electroformation setup.
with a spacer (~1 mm), then sealed with a vacuum grease (Dow Corning, High vacuum Grease). The chamber for was then filled with 2 ml of room-temperature deionized water. An AC signal of 10 Hz and 1.2 V (peak-to-peak) using a function generator (model 33250 A, Agilent, USA) was applied to the chamber for 2 h. During this process, lipiosomes grew on the substrate. Then, the AC signal was set to 4 Hz and 2.0 V (peak-to-peak) for 10min to detach the liposomes from the substrate in order to make an easy observation on a confocal microscope (Axiovert 100 M, Zeiss, German).
4. Experimental Results and Discussions
4.1. Egg-PC QLC
In order to checking this model, we checked over the QD size dependence for QD stabilization inside the lipid bilayer of liposome. The QLC is expected to be observed only for the QD size smaller than a certain specific size. We successfully obtained the blue-, green-and yellow-emission Egg-PC QLCs with clear and sharp fluorescent signals, as shown in Figure 5(a). However, when red-emission QDs were used with the same concentration as the blue-, green- and yellow-emission QDs during the QLC preparation, we did not obtain the red-emission DOPC QLCs. Instead, we observed some aggregation kind of image, as shown in Figure 5(b). The results are similar to those of previous DOPC experiments .
It means that the aggregated several QDs prefer to be surrounded by lipid instead of QLC. In other words, red-emission QDs were not incorporated into the bilayer of liposome. The experimental results are supporting the predictions of our theoretical model.
We believe that, if the QD radius is larger than , the QLC structure is no longer stable due to the high energy cost in the formation of either the lipid voids or increase of hydrophobic interface contacting with water, as shown in Figure 6. It means that the mono-layer curvature of surrounding the QD is highly required to form the QLC. In other words, we consider that hydrocarbon chain of Egg-PC lipids is not long enough, wetting a void formation at the ligand
Figure 5. (a) Confocal microscope image of the blue-, green-and yellow-emission QLC with core radius ~1.05 (nm), 1.25, 1.65 (nm) (b) Aggregated QD with core radius ~2.5 (nm) surrounding lipids is observed on the fluorescent microscopy. This scale bar is about 20 (μm).
Figure 6. The mono-layer deformation of positive curvature area induced CdSe surrounding by PC-type lipid.
portion that is connected with corner of the QD and the geometric shape of them don’t pack fully hydrophobic area deformed above . As a result, the QDs only below a certain specific size (core radius ≈ 1.8 nm) can stably reside in the lipid bilayer.
If lipids of large mono-layer curvature surrounding QD exist, they will reduce the deformation area and cover the void by highly curvature lipid. According to this model, , the specific radius of QD, is affected by a change in the minimum radius . In the case of Egg-PC lipid, the minimum of radius ( ) is given by Equation (6) and thus the maximum of radius curvature is . For forming the QLC above , it is necessary to use lipid having large monolayer curvature more than . It is theoretically difficult to reduce the curvature value of more than 1/10.8 nm−1 for a single lipid molecule of the PC type.
According to the experimental result by Israelachvili  , they have experimentally seen that it reduced the (non-spherical micelle) to the (spherical micelle) for sodium dodecyl sulphate surfactant (SDS) in water. Since and are fixed, the only way to reduce is to raise a0 by raising the pH of the solution. In practice, this could be achieved by increasing the pH of the solution. This would increase the degree of ionization of the negatively charged head-groups which increases the repulsion between them, resulting in an increase in a0. It means that the spherical micelle is more high curvature than non-spherical micelle. By Israelachvili’s experiment, in this study, we think that charged lipids (DOPG) with large optimal head area (a0) is able to from a highly mono-layer curvature more than by mixing the DOPC and DOPG.
4.2. DOPC/DOPG QLC
Figure 7 shows that is changed by the reduction of P value. Figure 7 is not a measured value but a calculated value by Figure 3(b), which the decrease of P resulted in the decrease of from Equation (6). The graph of Figure 3(b) shifted to the right due to the decrease of . This caused to shift to the
Figure 7. The change of critical point rcr according to changing P.
right. In other words, the reduction of can cause high curvature. It means that an increase in optimal head area (a0) results in highly curvature.
We seek to increase the large optimal head area (a0) to form a highly mono-layer curvature for checking the change of . In this study, if v and are fixed, the only way to reduce is to raise optimal head area (a0) by using the DOPG. We have the following experiment to confirm the increase of such as Figure 7.
As we mentioned earlier, QLC above will be formed by mixing DOPG with a charged heap-group and DOPC a neutral head-group for charge effect  .
We expected that this mixing would will be larger curvature than because of the increase of effective head-group area ( ), which arises from the repulsive interaction between the like-charged head-groups. It causes the geometry shape such as Figure 8(a). The phenomenon of effect head-group area explains as follows. For example, the micelle-forming lysolecithin ( ) and non-aggregate forming cholesterol ( ) will mix in certain proportions to form liposome ( ). If we mix DOPC and DOPG, we will expect that the mono-layer of the mixture of DOPC/DOPG lipids can form more a highly curvature mono-layer than Egg-PC mono-layer.
In this experiment, we observed the orange (radius; 2.0 - 2.15 nm) and red-emission QDs (radius ~2.5 nm) were successfully incorporated in the bilayer of the mixture of DOPC/DOPG lipids, as shown in Figure 8(b). This experiment result shows that the radius of curvature is increased by DOPG.
As we have anticipated the change of a specific point , this experimental result explains the increase in by the increase of by charge effect.
4.3. DOPC/DPPC QLC
In order to confirm charge effect of lipid head-group, experiments were conducted by mixing DPPC, a neutral lipid molecule, as a control experiment in the same manner as the above experiment. Figure 9 shows only the QLC below a specific QD size similar to the DOPC QLC experiment results.
Figure 8. (a) Geometric shapes of DOPG (truncated shape) and DOPC (truncated shape close to cylindrical shape) at a0; (b) Confocal microscopy image of the QLCs prepared with the same ratio of two lipids DOPC/DOPG (1:1) by using the orange and red-emission QDs (2 - 2.15 (nm) and ~2.5 (nm)). This scale bar is about 10 (μm).
Figure 9. QLC structure using DOPC/DPPC mixed lipid molecules in fluorescence microscopy. This scale bar is about 50 (μm).
In conclusion, it can be expected that the role of charge effect at the head-group is an important factor to form QLC structure above the specific QD size. In this study, unlike previous experimental results, we can observe the orange and red-emission QLC due to highly curvature mono-layer.
We proposed a simple model to describe the stability of QDs embedded in lipid bilayer in terms of molecular packing parameter and the conformational change of the lipid chain. The existence of QDs in the lipid bilayer was confirmed using confocal microscopy. QLC formation was found to be dependent on the size of QDs: Egg-QLCs formed with blue, green and yellow-emission QDs (core radius ~1.05 nm, 1.25 nm and 1.65 nm) but not with red-emission QDs (core radius ~2.5 nm). When DOPG lipids, which have a larger head group area, were mixed with DOPC lipids, QLCs were formed with orange-emission QDs as well as with red-emission QDs. The model predicts that 1) QDs below a certain critical size can stably reside in the lipid bilayer, and 2) the specific QD size increases as the head group area of the lipids increases. These predictions agree well with our experimental results in spite of a lack of exact information about the change of effect optimal head area and the conformational changes of the hydrocarbon chain around the QD.
This work was supported by a Research Institute for Convergence of Biomedical Science and Technology (30-2018-007), Pusan National University Yang-san Hospital.
*Contributed equally to this work.
#Corresponding author earlier know as Seong Jin Kim.