Specific Radius Change of Quantum Dot inside the Lipid Bilayer by Charge Effect of Lipid Head-Group

We studied the quantum dot-liposome complex (QLC), which is the giant unilamellar vesicle with quantum dots (QDs) incorporated in its lipid bilayer. A spin coating method in conjunction with the electroformation technique yielded vesicles with highly homogeneous unilamellar structure. We observed QD size dependence of the QLC formation: QLCs form with blue, green and yellow-emission QD (core radius ~1.05 nm, 1.25 nm and 1.65 nm) but not with red-emission QD (core radius ~2.5 nm). In order to explain this size dependence, we made a simple model explaining the QD size effect on QLC formation in terms of the molecular packing parameter and the lipid conformational change. This model predicts that QDs below a certain critical size (radius ≈ 1.8 nm) can stably reside in a lipid bilayer of 4 - 5 nm in thickness for Egg-PC lipids. This is consistent with our previous experimental results. In the case of red-emission QD, QD-aggregations are only observed on the fluorescent microscopy instead of QLC. We expected that the reduction of packing parameter (P) would lead to the change of specific QD radius. This prediction could be verified by our experimental observation of the shift of the specific QD size by mixing DOPG.


Introduction
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 [1] 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 [2]- [11]. One good example is QLC (Quantum dot-Liposome Complex) which is a giant unilamellar vesicle with QDs incorporated in the lipid bilayer [12] [13] [14] [15].
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 [12]. 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 [16].
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 [13] [14]. 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 [15].  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.

Background and Model
According to Israelachvili's work [17], given the packing parameter P of a given lipid, the minimum radius min R of the special liposome is determined as follow. Figure 2 shows a uni-bilayer liposome with the in-outer layer ( 0 R ) and the outer layer thickness ( 0 t ) in a single liposome. For liposome of the outer layer volume 0 V and the outer surface area 0 S with 0 N molecules, there are following relations between them [18].

( )
Here, v is the volume of simple hydrocarbon molecule. The area per head group (a) is Open Journal of Biophysics ( ) Here, ( 0 a a ≠ ) is the actual area per head group. If Equation (3) is divided by a 0 , the ratio of the actual area a to the optimal area a 0 is given by Here, a 0 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 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 c l 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 [17] Tanford [19] and Lindman [20]. c l for the saturated hydrocarbon chains is Here, max l 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, c l is of the same order as, though somewhat less than, the fully extended molecular length of the chain max l . It can be seen that the minimum size of a liposome ( min R ) depends on the packing parameter (

Modeling
The key point of this model would define the critical QD radius by limiting the max l to cover part of the void around the QD max S at graph. For the definition of max S in this model, we considered only the size of QD core excluding ligand (hexadecylamine).
Equation (6) shows the minimum possible radius min R 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 min 1 R to evade any unfavorable surface energy penalties. In other words, min R 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 min R , as in our experiment, the curvature of the monolayer around the QD is approximated as min 1 R , and the deformed monolayer profile is a circular arc of radius as min R shown in Figure 4. In the case of Egg-PC lipid liposome, the packing parameter value is known to be 0.85 ( [17]. Therefore, we know that min R 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 max 2.43 nm l = 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 Open Journal of Biophysics Equation (8) is differentiated with respect to θ to obtain the minimum max S 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 max S as a function of the QD radius r. max S can't exceed the maximally stretched chain length, ligand length (~1 nm) plus max l , which is 3.43 nm in this case [17]. 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 1.8 nm cr r ≈ , where the chain is maximally stretched to max S (corresponding to the horizontal dashed line in Figure 3(b)).
In Figure 3

Preparation of QLC
QLCs were synthesized by using the mixed solutions of QDs and phospholipids via the electroformation method [22] in conjunction with spin-coating technique [23], as shown in

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 [15].
It means that the aggregated several QDs prefer to be surrounded by lipid in-  portion that is connected with corner of the QD and the geometric shape of them don't pack fully hydrophobic area deformed above cr r . 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, cr r , the specific radius of QD, is affected by a change in the minimum radius min R . In the case of Egg-PC lipid, the minimum of radius ( min :10.8 nm R ) is given by Equation (6)  According to the experimental result by Israelachvili [17], they have experimentally seen that it reduced the 0.37 P ≈ (non-spherical micelle) to the 0.33 P ≈ (spherical micelle) for sodium dodecyl sulphate surfactant (SDS) in water. Since ν and c l are fixed, the only way to reduce is to raise a 0 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 a 0 . 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 (a 0 ) is able to from a highly mono-layer curvature more than min 1 R by mixing the DOPC and DOPG. Figure 7 shows that cr r 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 min R from Equation (6). The graph of Figure 3(b)

DOPC/DOPG QLC
shifted to the right due to the decrease of min R . This caused cr r to shift to the Open Journal of Biophysics right. In other words, the reduction of min R can cause high curvature. It means that an increase in optimal head area (a 0 ) results in highly curvature.
We seek to increase the large optimal head area (a 0 ) to form a highly mono-layer curvature for checking the change of cr r . In this study, if v and c l are fixed, the only way to reduce 0 c P v a l = is to raise optimal head area (a 0 ) by using the DOPG. We have the following experiment to confirm the increase of cr r such as Figure 7.
As we mentioned earlier, QLC above cr r will be formed by mixing DOPG with a charged heap-group and DOPC a neutral head-group for charge effect [17] [24].
We expected that this mixing would will be larger curvature than min 1 R because of the increase of effective head-group area ( 0 e a ), which arises from the repulsive interaction between the like-charged head-groups. It causes the geometry shape such as Figure 8 c v a l < < ). 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.

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. Open Journal of Biophysics  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.

Conclusion
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 Open Journal of Biophysics ~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.